# Abdul-Majid Wazwaz's research while affiliated with Saint Xavier University and other places

## Publications (653)

Article
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In this study, an effective iterative technique based on Green’s function is proposed to solve a nonlinear fourth- order boundary value problem (BVP) with nonlinear boundary conditions, which models an elastic beam. An iterative Green’s function approach and a shooting method are integrated in the proposed method. The mathematical derivation is fur...
Preprint
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In this paper, an integrable generalization of the Kadomtsev-Petviashvili (KP) equation in arbitrary spatial dimension is proposed. Firstly, the singularity manifold analysis is performed to prove that the (n+1)-dimensional KP equation with general form is Painleve integrable. Secondly, combining the truncated Painleve expansion and binary Bell pol...
Article
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In this work, a damped modified Kawahara equation (mKE) with cubic nonlinearity and two dispersion terms including the third- and fifth-order derivatives is analyzed. We employ an effective semi-analytical method to achieve the goal set for this study. For this purpose, the ansatz method is implemented to find some approximate solutions to the damp...
Article
Purpose This paper aims to propose a new (3+1)-dimensional integrable Hirota bilinear equation characterized by five linear partial derivatives and three nonlinear partial derivatives. Design/methodology/approach The authors formally use the simplified Hirota's method and lump schemes for determining multiple soliton solutions and lump solutions,...
Article
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This article investigates nonlinear behavior of ion acoustic waves in a plasma with superthermal electrons and isothermal positrons. We consider the KdV–Burgers equation with dissipation in dusty plasmas and construct Lie symmetries, infinitesimal generators and commutative relations under invariance property of Lie groups of transformations. The a...
Article
The current work proposes a new (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation ((3+1)-KPE). We verify the integrability of this equation using the Painlevé analysis (PA). The bilinear formula is applied to the extended KPE to explore multiple-soliton solutions. Also, we formally establish a class of lump solutions using distinct values of...
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In this work, we develop a new (3+1)-dimensional Sakovich equation to describe nonlinear wave propagation. We use the truncation expansion method to confirm the Painlevé integrability of the newly established equation. Then, its general soliton solution and multiple-soliton solutions are constructed. We also verify that the equation possesses solit...
Article
In this study, the coupled nonlinear (1+1)-dimensional Drinfel’d-Sokolov-Wilson (DSW) equation in dispersive water waves is investigated. \textcolor{red} {The proposed structure is very important nonlinear evolution model in mathematical physics and engineering, which is used to describe nonlinear surface gravity wave propagating over horizontal se...
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The current work introduces two extended (3 + 1)- and (2 + 1)-dimensional Painlevé integrable Kadomtsev–Petviashvili (KP) equations. The integrability feature of both extended equations is carried out by using the Painlevé test. We use the Hirota’s bilinear strategy to explore multiple-soliton solutions for both extended models. Moreover, we formal...
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The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, an...
Article
In this work, the non-integrable nonplanar (cylindrical and spherical) damped Kawahara equation (ndKE) is solved and analyzed analytically. The ansatz method is implemented for analyzing the ndKE in order to derive some high-accurate and more stable analytical approximations. Based on this method, two-different and general formulas for the analytic...
Article
In this research, discrete singular convolution, that depends on Regularized Shannon kernel, is used to look for the efficient solution of (4 + 1) dimensional nonlinear Fokas equation. The governing system of nonlinear five-dimensional Fokas equation is transformed into a system of nonlinear ordinary differential equations via discrete singular con...
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In this article, the generalized breaking soliton equation is considered which demonstrates the intersections of the surface wave dispersion curve and the complex-zone border in a weakly magnetic plasma. Firstly, the Hirota bilinear method is employed to determine the bilinear form of given model. Consequently, the lump wave solutions, collision of...
Article
In this study, the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation is investigated via two diverse techniques. Firstly, we retrieve the bilinear form of given equation by utilizing Hirota bilinear method. Consequently, the lump waves and collisions among lumps and periodic waves, the collision...
Article
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The current study is dedicated to furnish a class of bright soliton and dark soliton solutions for the (3+1)-dimensional hyperbolic nonlinear Schrödinger equation. In this direction we operate with a variety of schemes to derive a class of bright and dark optical soliton solutions. Moreover, we derive another class of solutions of distinct structur...
Article
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This work is dedicated to a ($$3+1$$)-dimensional modified Ito equation of seventh order. The standard integrable ($$3+1$$)-dimensional Ito equation of seventh order is established as well. Painlevé analysis is used to test the complete integrability of the extended models. Three branches of resonance points are derived for each model. Multi-solito...
Article
Purpose The purpose of this paper is to study an extended hierarchy of nonlinear evolution equations including the sixth-order dispersion Korteweg–de Vries (KdV6), eighth-order dispersion KdV (KdV8) and many other related equations. Design/methodology/approach The newly developed models have been handled using the simplified Hirota’s method, where...
Article
In this study, we have improved the long-wave limit method to efficiently derive higher-order rogue waves for (1+1)-dimensional integrable systems. By taking the nonlinear Schrödinger equation as an example, the results obtained by this method are consistent with those obtained by other known methods, such as the generalized Darboux transformation...
Article
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In this work, we study an extended integrable (3+1)-dimensional Ito equation, where its complete integrability is justified via Painlevé analysis. The simplified Hirota’s method is used to formally derive multiple-soliton solutions. Moreover, we obtain a general class of lump solutions by using symbolic computation with Maple. Lump solutions are fu...
Article
In this paper, we provide a generating mechanism to obtain rogue wave solutions from N soliton of Hirota's bilinear method. Based on the long wave limit method, the phase parameters are reconstructed to generating rogue wave solutions of Korteweg–de Vries Benjamin-Bona-Mahony equation. The rogue wave solutions are expressed explicitly in rational f...
Article
This course of research is dedicated to Biswas-Milovic (BM) model with variable coefficients comprising Kerr law and damping effect. More precisely, Biswas-Milovic (BM) equation is mathematical framework for depicting soliton transmission via optical wave guides in more general sense. Bright, dark and singular soliton solutions to the governing equ...
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In this work, the Lakshmanan-Porsezian-Daniel model is investigated which is the generalization of the non-linear Schrödinger model, to describes the dynamical behavior of optical solitons. The extended modified auxiliary equation mapping method is employed to develop some new exact solitary wave solutions to the complex model with the ker law, the...
Article
In this work, we employ the potential similarity transformation method to derive some solitary wave packet solutions for the Calogero-Bogoyavlenskii-Schiff (CBS) equation. Exploiting nonsingular local multipliers, a set of local conservation laws is presented for the equation. The nonlocally related partial differential equation (PDE) systems were...
Article
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The goal of this work is to solve an initial-value problem for a fractional differential equation that governs the ray tracing through a crystalline lens using an interesting variation of the Adomian decomposition method. A new recursive scheme is presented by combining the Adomian decomposition method with a formula and via the solutions of the we...
Article
In this investigation, both bright and dark envelope optical solitons to a (2+1)-dimensional cubic nonlinear Schrödinger equation (cNLSE) are examined. We employ distinct powerful ansatze to obtain exact analytical bright soliton and dark soliton solutions to the mentioned model, which is characterized by cubic nonlinearity. Furthermore, some other...
Article
In this work, new [Formula: see text]-dimensional Korteweg–de Vries (KdV) equation and modified KdV (mKdV) equation as well as the corresponding fractional forms are presented. These two equations are derived for the first time relying on the extended [Formula: see text]-dimensional zero curvature equation. In addition, symmetries and conservation...
Article
In this paper, the symmetry method and generalized Kudryashov method are utilized for constructing new dynamic exact solutions to a (3+1)-dimensional potential Calogero–Bogoyavlenskii–Schiff equation (CBS) equation. The symmetry method was employed to obtain symmetry vectors and symmetries to use it for reducing the governing equation for various t...
Article
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In this work, we examine various physical phenomena modeled by nonclassical boundary value problems with nonlocal boundary conditions. We concern our analysis on a new type of nonlocal boundary value problems, i.e., the semi-numerical solution of the generalized Thomas–Fermi type equations and Lane–Emden–Fowle type equations subjected to integral t...
Article
In this article, we suggest a new form of modified Kudryashov’s method (NMK) to study the Dual-mode Sawada Kotera model. We know very well that the more the solutions depend on many constants, the easier it is to study the model better by observing the change in the constants and what their impact is on the solutions. From this point of view, we de...
Preprint
In this paper, a new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed. Its integrability is verified by the Painlev\’e analysis. The bilinear form, multiple-soliton, breather and lump solutions are obtained via using the Hirota bilinear method. Furthermore, the abundant dynamical behaviors for these solutions are discovered...
Article
Hybrid nanofluid becomes a fascinating research topic due to its thermophysical properties and stability which provide better performance compared to typical nanofluids. Two-phase model for mixed convection magnetohydrodynamic (MHD) flow was investigated incorporating hybrid nanoparticles of Alumina (Al2O3) and Copper (Cu) while the base fluid is w...
Article
In this work, a two coupled nonlinear Schrödinger equation (CNLSE) which is applicable to high birefringence fibers is investigated. We operate a variety of ansatze to derive a variety of bright and dark optical envelope soliton solutions. Also, other solutions of distinct structures, periodic, exponential, and singular, are derived. This analysis...
Article
A skillful partial limit approach is proposed in this paper, which is used to generate some new solutions called multiple-pole solutions directly from the well-known N-soliton solution for the fifth-order modified Korteweg–de Vries equation. Based on the traditional limit method developed by us, the dark double-pole solution neglected by some schol...
Article
Differential equations play an important role in many scientific fields. In this work, we study modified Gardner-type equation and its time fractional form. We first derive these two equations from Fermi-Pasta-Ulam (FPU) model, and found that these two equations are related with nonlinear Schro¨dinger equation (NLS) type of equations. Subsequently,...
Article
Purpose This study aims to introduce a variety of integrable Boussinesq equations with distinct dimensions. Design/methodology/approach The author formally uses the simplified Hirota’s method and lump schemes for exploring lump solutions, which are rationally localized in all directions in space. Findings The author confirms the lump solutions fo...
Article
In this paper, the exact solutions to the AB nonlinear system are investigated. This system is reduced via two different transformations to a sine-Gordon equation and a quasilinear equation for a new dependent variable ϕ. Solutions to a sine-Gordon equation and a quasilinear equation are found. Hence, the original system can well be solved for such...
Article
In this work, we study multi-point singular boundary value problems (BVPs) that received considerable interest in various scientific and engineering applications. We focus this study on obtaining approximate solutions, particularly of the three-point generalized Thomas–Fermi and Lane–Emden–Fowler BVPs. Our algorithm employs two main steps. We first...
Article
In this work, we study an extended (2+1)-dimensional perturbed nonlinear Schrödinger equation (P-NLS) with Kerr law nonlinearity in a nano optical fiber. The extended model includes fourth-order spatial derivatives. We study the influence of the nonlinearity and spatial dispersions effects given in spatial directions x and y. Various types of optic...
Article
Based on the reduced version of the Grammian form, a lump molecule, a bound state of lump waves, is obtained for the famous Kadomtsev-Petviashvili I system. In this study, the coordinates of lump waves in molecules are explicitly given in order to accurately describe asymptotic behavior of a lump molecule. And the dynamic properties of a lump molec...
Article
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In this work, we study the dynamical behavior for a real physical application due to the inhomogeneities of media via analytical and numerical approaches. This phenomenon is described by the 3D Date-Jimbo-Kashiwara-Miwa (3D-DJKM) equation. For analytical techniques, three different methods are performed to get hyperbolic, trigonometric and rational...
Article
We employ numerical methods to investigate the dissipative freak waves (FWs) and dissipative breathers (Bs) in collisional electronegative complex plasmas. The plasmas under investigation possess inertialess Maxwellian thermal electron and light negative ion in addition to stationary negatively charged dust grains. To achieve this goal, we reduce t...
Article
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Under investigation in this paper is the AB system, which is used to describe the propagation of the wave packets in a marginally stable or unstable baroclinic shear flow. Introducing an auxiliary function a(t),we predict irregular solitons and construct the high-order irregular dark solitons for the AB system,which are different fromthose in the e...
Article
The article studies the dynamics of Gaussian solitary waves in nano optical fibers which are described by perturbed and improved nonlinear Schrödinger equations which have logarithmic nonlinearities with and without attenuation terms. As a result, the Gaussian solitary waves have been extracted for the logarithmic perturbed nonlinear Schrödinger eq...
Article
Space-time conformable fractional nonlinear (1+1)-dimensional Schrödinger-type models are investigated in this paper. Traveling wave solutions using the sine-Gordon expansion approach for these models are presented. The sine-Gordon expansion method is used to obtain exact solutions for three types of space-time conformable fractional nonlinear Schr...
Article
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This work deals with a new $$(3+1)$$-dimensional Painlevé integrable fifth-order equation characterized by third-order temporal and spatial dispersions. The Painlevé test is carried out to demonstrate the complete integrability of this model. A rule that governs the dispersion relation with the spatial variables coefficients is reported. We employ...
Article
In this work we examine an extended nonlinear (2+1)-dimensional Sasa-Satsuma equation that covers the effect of perturbations. The extended model includes fourth-order spatial derivatives. We study the influence of the nonlinearity and spatial dispersions effects given in spatial directions x and y. We formally derive a variety of optical soliton s...
Article
Purpose This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t . The new equation models both right- and left-going waves in a like manner to the Boussinesq equation. Design/methodology/approach This formally uses the simplified Hirota’s method and lump schemes for...
Article
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Nonlinear shock waves in plasma was modeled and studied using Ramani equation of sixth order and its coupled form representing the interaction between two waves. A new combined methodology of both Lie infinitesimal transformation and singular manifold methods was exploited to create analytical solutions. The method was extended to investigate a cou...
Article
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In this work, we study the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation. We employ the extended tanh function method and the simple equation method to achieve analytical soliton solutions. Moreover, numerical treatment for this equation is introduced by the finite difference method. We justify the accuracy of the obtained results b...
Article
In this paper, the integrable (4 + 1)-dimensional Fokas equation is investigated. Exploiting a set of non-singular local multipliers, we present a set of local conservation laws for the equation. The nonlocally related partial differential equation (PDE) systems are found. Nine nonlocally related systems are discussed reveal thirty five interesting...
Article
Bifurcation is one of the most common phenomena in nature. We report a class of novel bifurcation phenomena in fluids by studying the bifurcation soliton solutions of an extended Kadomtsev–Petviashvili equation. By introducing the bilinear method and choosing appropriately the auxiliary function involved in the bilinear form, new soliton solutions...
Article
In this paper, the coupled Manakov equations with variable coefficients, governing the orthogonally polarized pulses transmission in two mode optical fibers, are studied via the Hirota method. The double-hump one- and two-soliton solutions of the Manakov equations are obtained for the first time. Furthermore, the v-type, parabolic, s-type double-hu...
Article
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Space-time conformable fractional nonlinear ( 1 + 1 )-dimensional Schrödinger-type models are investi- gated in this paper. Traveling wave solutions using the sine-Gordon expansion approach for these models are presented. The sine-Gordon expansion method is used to obtain exact solutions for three types of space-time conformable fractional nonlinea...
Article
In this work we present a generalized nonlinear (3+1)-dimensional Sasa-Satsuma equation. This equation is influenced by nonlinearity and spatial dissipations effects in all spatial directions. We formally retrieve bright and dark optical soliton solutions for this higher dimensional Sasa-Satsuma model. In addition, other singular and exponential so...
Article
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In this paper, we consider Lane–Emden problems which have many applications in sciences. Mainly we focus on two special cases of Lane–Emden boundary value problems which models reaction–diffusion equations in a spherical catalyst and spherical biocatalyst. Here we propose a method to obtain approximate solution of these models. The main reason for...
Article
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In this work, we develop two new (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlevé integrability test via examining the compatibility conditions for each developed model. We examine the dispersion relation and der...
Article
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The current work is devoted for operating the Lie symmetry approach, to coupled complex short pulse equation. The method reduces the coupled complex short pulse equation to a system of ordinary differential equations with the help of suitable similarity transformations. Consequently, these systems of nonlinear ordinary differential equations under...
Article
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility by the properties of nonlinear hydrodynamics. In this present work, numerous group-invariant solutions of the (3+1)-dimensional KdV-type equation are derived with the virtue of Lie symmetry analysis. Also, we obtain the corresponding infinites...
Article
Purpose This study aims to develop two integrable shallow water wave equations, of higher-dimensions, and with constant and time-dependent coefficients, respectively. The author derives multiple soliton solutions and a class of lump solutions which are rationally localized in all directions in space. Design/methodology/approach The author uses the...
Article
The modified decomposition method is applied to analyze the transverse vibrations of tapered rotating beams incorporating both axial centrifugal stiffening and flexible end constraints. Unlike prior analyses relying upon a power series expansion about the left end constraint, we instead expand the solution for the transverse deflection about the in...
Article
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In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of overning equation via using the Painlevé analysis. We next reduce the KP equation to a one-dimensional with the help of Lie symmetry analysis (LSA). The KP equation reduces to an ODE b...
Article
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In this paper, we develop a new extended Kadomtsev–Petviashvili (eKP) equation. We use the Painlevé analysis to confirm the integrability of the eKP equation. We derive the bilinear form, multiple soliton solutions and lump solutions via using the Hirota’s direct method. Moreover, the soliton, breather and lump interaction solutions for this model...
Article
In this work we address a new (3+1)-dimensional nonlinear Schrödinger equation influenced by cubic nonlinearity and spatial dissipations effects. We formally retrieve bright and dark optical soliton solutions for this higher dimensional Schrödinger model. In addition, other singular and periodic solutions of distinct structures are derived.
Preprint
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In this work, we develop two new (3+1)-dimensional KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlev´e integrability test via examining the compatibility conditions for each developed model. We examine the dispersion relation and de...
Article
A complex tanh-function method is presented for constructing optical soliton solutions for quadratic–cubic nonlinear medium. In addition, an ansätze is proposed for obtaining soliton solutions of the dimensionless form of the nonlinear Schrödinger’s equation that governs the propagation of solitons through optical fibers.
Article
This work introduces two new sixth-order (3+1)-dimensional nonlinear Schrödinger equations with higher-order dispersive terms influenced by cubic-quintic-septic (CQS) nonlinearities. We formally retrieve bright and dark optical soliton solutions for each higher dimensional model. In addition, we find certain constraints on the parameters to determi...
Article
In this paper, a new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed. Its integrability is verified by the Painlevé analysis. The bilinear form, multiple-soliton, breather and lump solutions are obtained via using the Hirota bilinear method, a symbolic computation scheme. Furthermore, the abundant dynamical behaviors for t...
Article
In this work, the three-dimensional unsteady flow was scrutinized adjacent to a flat plate immersed inside a fluid with electric conductivity in the presence of constant magnetic field. An extended model of group transformation method was exploited, comprising three parameters, to transform the mathematical model into a new system of ordinary diffe...
Article
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Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) interaction solutions between lump wave and solitary waves; (iii) interaction solutions between lump wave and periodic waves; and (iv) breather wave solutions. Furthermore , graphical representation o...
Article
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The aim of this paper is to present a new method and the tool to validate the numerical results of the Volterra integral equation with discontinuous kernels in linear and non-linear forms obtained from the Adomian decomposition method. Because of disadvantages of the traditional absolute error to show the accuracy of the mathematical methods which...
Article
In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for...
Article
In this work, we study the double chain Deoxyribonucleic acid (DNA) model, the study will be carried out by using two analytical methods, namely, Lie transformation method, then combined with the singular manifold method (SMM). Six cases are studied for different vector combinations. Two successive symmetry reductions transform the equation to an o...
Article
Purpose This paper aims to develop a new (3 + 1)-dimensional Painlev´e-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model. Design/methodology/approach This paper uses the simplified Hirota’s method for deriving multiple soliton solutions. Findings This paper finds that the develo...
Preprint
Under investigation is a (3+1)-dimensional generalized breaking soliton equation in nonlinear media. The interaction solution between lump wave and N-soliton (N = 2,3,4) are derived. The interaction solution between lump wave and periodic waves is also studied. Breather-wave and multi-wave solutions are obtained. The dynamical behavior is demonstra...
Article
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In this paper, we construct an extended Bogoyavlenskii‐Kadomtsev‐Petviashvili (eBKP) equation. We use the Painlevé analysis to justify the integrability of the eBKP equation. We also examine the integrability of a related extended CBS equation. We derive multiple soliton solutions via using the Hirota's direct method. In addition, a variety of exac...
Article
A reductive perturbation technique (the derivative expansion technique (DET)) is employed to derive a linear damped nonlinear Schrödinger equation (LDNLSE) for investigating the feature properties of the dissipative modulated nonlinear dust-acoustic wavepacket including rogue waves (RWs) in an electron-ion dusty plasma having superthermal electrons...
Article
This work addresses the soliton propagation for a sixth-order (3+1)-dimensional nonlinear Schrödinger equation with fourth-order and sixth-order dispersive terms under the influence of cubic–quintic–septic nonlinearities. We formally retrieve bright and dark optical soliton solutions for this equation. In addition, we find certain constraints on th...
Article
In this work, we study an extended (3+1)-dimensional Jimbo-Miwa equation. We analyze the dynamics of three-dimensional nonlinear ion-acoustic waves in an unmagnetized plasma. We furnish the Lie symmetry technique to investigate the symmetry reductions of the examined model. The arbitrary functions involved in the Lie vectors are secured by using an...
Article
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The area of telecommunications has experienced a considerable growth in the last few decades due to remarkable development in the field of optical fibers. Optical solitons form the basic fabric in the area of telecommunication industry. The captivating technology of sub-pico second pulses that propagate through optical fibers is modeled with Kaup-N...
Article
In this article, we utilize the generalized exponential rational function method and obtain exact solitary wave solutions in various forms of the strain wave equation. Abundant exact solitary solutions including multiple-solitons, bell-shaped solitons, traveling waves, trigonometric and rational solutions have been constructed. The dynamical struct...
Article
Purpose This study aims to develop a new (3 + 1)-dimensional Painlevé-integrable extended Vakhnenko–Parkes equation. The author formally derives multiple soliton solutions for this developed model. Design/methodology/approach The study used the simplified Hirota’s method for deriving multiple soliton solutions. Findings The study finds that the d...
Article
Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear...
Article
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In this present article, we devote our study on (2+1)-dimensional Nizhnik-Novikov-Vesselov (NNV) equations. To achieve our goal, we utilize various mathematical methods, namely Lie symmetry method, the Exp-function method and N-soliton solutions methods, and attain exact analytical solutions in numerous forms of the NNV system. Firstly, we generate...
Article
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The current study is dedicated for operating the Lie symmetry approach, to complex short pulse equation. The method reduces the complex short pulse equation to a system of ordinary differential equations with the help of suitable similarity transformations. Consequently, these systems of nonlinear ordinary differential equations under each subalgeb...
Article
Full-text available
The mathematical discontinuity existing in the phase-difference dynamic model for the Josephson junction results in the challenge of the dynamic analysis on the Josephson junction. Focusing on the non-smooth characteristics of the dynamic model for the long 0-π Josephson junction, two typical local dynamic behaviors, including the moving breather a...
Article
We develop two (3+1)-dimensional Date–Jimbo–Kashiwara–Miwa equations, characterized with constant and time-dependent coefficients. We furnish Painlevé analysis to show that each equation is completely integrable in the Painlevé sense. We show that these equations admit multiple soliton solutions. Furthermore, mixed solutions consisting of solitonic...
Article
In this paper, we are concerned with a higher order nonlinear Schrödinger equations existing in the anomalous dispersion regimes and the normal dispersive regimes. Applying the variational iteration method (VIM) we present bright soliton solutions for the anomalous case and dark optical soliton solutions for the normal dispersive regime. We address...
Article
Forward scattering of (3 + 1)-dimensional Jimbo-Miwa (JM) equation is investigated by singular manifold method (SMM). The detected Lax pair is reduced through three parameters group method into a compatible couple of ordinary differential equations (ODEs). Three forms of symmetry variables have been discussed leading to integrable system of ODEs. S...
Article
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A new nonlinear integrable fifth-order equation with temporal and spatial dispersion is investigated, which can be used to describe shallow water waves moving in both directions. By performing the singularity manifold analysis, we demonstrate that this generalized model is integrable in the sense of Painlevé for one set of parametric choices. The s...