Jalil Manafian

• PhD
• Department of mathematics at University of Tabriz

Citation: Deka, M.K.; Pradhan, B.; Dev, A.N.; Mahanta, D.; Manafian, J.; Mahmoud, K.H. Shock Waves in Ion-Beam-Depleted Spin-Polarized Quantum Plasma with Ionic Pressure Anisotropy. Plasma 2025, 8, 3. Abstract: In this study, the effects of pressure anisotropy and viscosity on the propagation of shock waves in spin-polarized degenerate quantum magn...

In this article, the spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time. In this framework, the Hirota bilinear form is applied to acquire diverse types of breather wave solutions from the foresaid equation. Ab...

In this research, the exact solitons to an important wave equation, namely, the quartic Rosenau-Kawahara-Regularized-Long-Wave (QRKRLW) equation are obtained along with an effective definition of fractional derivative, Truncated M-fractional. This model has much importance in fluid dynamics, shallow waves, and many others. For our this purpose, two...

In this paper, the thin-film ferroelectric material equation which enables a propagation of solitary polarization in thin-film ferroelectric materials, and it also can be described using the nonlinear evolution equations. Ferroelectrics are dielectric materials explain wave propagation nonlinear behaviors. Thin films made from the ferroelectric mat...

In this article, the potential Kadomtsev-Petviashvili (pKP) type coupled system with variable coefficients is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time. In this framework, Hirota bilinear form is applied to acquire diverse types of interaction lump solutions from the foresa...

In this work, numerous rogue wave solution strategy (MRWSS) agreeing to the Hirota bilinear hypothesis is utilized. The said strategy to build different soliton wave solutions for the generalized Hirota-Satsuma-Ito (GHSI) condition is considered. These numerous soliton wave solutions incorporate first-order, second-order, third-order, and fourth-or...

In this research article, the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrödinger equations (CNLSEs) are studied, which play an important role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Our primary goal is to obtain the analytical solutions utilizing novel methodology, particularly the modified...

We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions...

In this paper, a non-autonomous (3+1) dimensional coupled nonlinear Schrödinger equation (NLSE) with variable coefficients in optical fiber communication is analyzed. By means of bilinear technique and symbolic computations, new multi-soliton solutions of the coupled model in different trigonometric and lump functions are given. Then, in terms of p...

In this study, an efficient numerical method is applied to KdV-Burger-Fisher equation which is one of the dispersion-dissipation–reaction model. The present method is based on the collocation method whose weight functions are taken from the family of the Dirac delta functions in finite element methods. The element functions are selected as quintic...

The study consists of the distinct types of the exact soliton solutions to an important model called the beta-time fractional (1 + 1)-dimensional non-linear Van der Waals equation. This model is used to explain the motion of molecules and materials. The Van der Waals equation explains the phase separation phenomenon. Noncovalent Van der Waals or di...

In this work, we have studied the propagation of nonlinear electrostatic shock waves in an anisotropically pressured magnetized plasma containing positive and negative ions, trapped electrons, and positrons. A reductive perturbation technique is used to generate the trapped Zakharov-Kuznetsov Burgers’ equation is generated for nonlinear analysis. W...

In this paper, the thin-film ferroelectric material equation (TFFME), which enables the propagation of solitary polarisation in thin-film ferroelectric materials is investigated, will be expressed through the non-linear evolution models. Ferroelectrics are dielectric materials that explain wave propagation non-linear demeanors. The non-linear wave...

In this work, the exact solutions of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equation are reported by adopting the He’s variational direct technique (HVDT). The analytic findings of solutions were obtained by semi-inverse scheme, and six form of supposed studies reveal that the solutions belong to soliton groups. The modulation instabi...

In this article, a variable-coefficient Kadomtsev–Petviashvili (VCKP) equation is studied by using the Hirota technique. The formulae of the bilinear equation via the bilinear transformation are obtained. Also, the new exact homoclinic, improved homoclinic, and generalized homoclinic solutions for the VCKP equation are investigated. Exclusively, th...

The dissipation effect in the viscous plasma is expressed in the current study by a Burgers term. The Weighted Residual Method is used to produce a solitary type progressive wave solution for very small values of the Burgers term. However, the strong dissipation may cause the origination of a shock solution. An approximate analytical solution is al...

The Gilson–Pickering equation, which describes wave propagation in plasma physics and the structure of crystal lattice theory that is most frequently used. The discussed model is converted into a bilinear form utilizing the Hirota bilinear technique. Sets of case study are kink wave solutions; breather solutions; collision between soliton and perio...

In this paper, the Gilson-Pickering equation which enables a wave propagation in plasma physics and crystal lattice theory is studied. Based on the auxiliary transformation, the sets of the nonlinear form of ODE along with some analytic solutions are deriven. Multi wave solutions containing one-, two- and three-waves are obtained. The characterizat...

In this research, the solitary wave solutions, the periodic type, and single soliton solutions are attained. The coupled fractional Lakshmanan–Porsezian–Daniel (LPD) equation is depicted the wave pulses’ physical properties in birefringent optical fibres containing two vector solitons. Here, the Paul–Painlevé operator is employed to investigate kin...

In this work, we have examined the propagation of nonlinear electrostatic shock waves in an anisotropically pressured magnetised plasma including positive and negative ions, trapped electrons, and positrons. Using a reductive perturbation technique, the trapped Zakharov-Kuznetsov Burger (TZK-B) equation is generated for nonlinear analysis. We study...

This article discusses the solitons as well as additional solutions to the modified nonlinear Schrödinger equation, which appears in the study of optical waveguide and rogue waves in ocean. One theorem is analyzed and and also is investigated by obtaining one solution as exact optical soliton solution from the modified NLSE utilizing the Paul-Painl...

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the sup...

We focused on solitonic phenomena in substrate-supported graphene sheets by learning the solitons of fractional thermophoretic motion equation, which was extracted from wrinkle wave motions. By utilizing the analytical technique and selecting suitably the improved tan(ϕ/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usep...

This paper presents many new soliton solutions in equation of nano-ionic currents along microtubules using an improved tan(ϕ/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docu...

This study is focusing on the integrable (3+1)-dimensional equation that combines the potential Kadomtsev-Petviashvili (pKP) equation with B-type Kadomtsev-Petviashvili (BKP) equation, also known as the pKP-BKP equation. The idea of combining integrable equations has the potential to produce a variety of unexpected outcomes such as resonance of sol...

In this article, the (2+1)-dimensional KdV equation by Hirota’s bilinear scheme is studied. Besides, the binary bell polynomials and then the bilinear form is created. In addition, an interaction lump with k k -soliton solutions of the addressed system with known coefficients is presented. With the assistance of the stated methodology, a cloaked fo...

In this paper, the M-lump solutions, the periodic type, and cross-kink wave solutions are acquired. Here, the Hirota bilinear operator is employed. By utilizing the symbolic computation and employing the utilized method, the (3+1)-dimensional Jimbo–Miwa (JM) equation is investigated. Based on the Hirota bilinear form, the soliton solution and perio...

In this paper, the new optical wave solutions to the truncated M-fractional (2 + 1)-dimensional non-linear Schrödinger’s complex hyperbolic model by utilizing the generalized Kudryashov method are obtained. The obtained solutions are in the form of trigonometric, hyperbolic and mixed form. These solutions have many applications in nonlinear optics,...

In this paper, the solitary wave solutions, the periodic type, and single soliton solutions are acquired. Here, the Hirota bilinear operator is employed to investigate single soliton, periodic wave solutions and the asymptotic case of periodic wave solutions. By utilizing symbolic computation and the applied method, generalized (3+1)-dimensional sh...

In this paper, the exact solitary wave solutions for the generalized nonlinear (NL) Schrödinger equation with parabolic NL law employing the generalized [Formula: see text]-expansion technique, the improved [Formula: see text]-expansion technique and the modified exp-function technique are acquired. Different sets of exponential function solutions...

In this paper, the nonparaxial solitons in a dimensionless coupled nonlinear Schrödinger system with cross-phase modulation, which enables the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide are studied. By noticing that the system is a non-integrable one, and also diverse forms of solitary wave solutions by using...

In this paper, the thin-film ferroelectric material equation (TFFME) which enables the propagation of solitary polarization in thin-film ferroelectric materials is investigated, and also illustrated through the nonlinear evolution equations. Ferroelectrics are dielectric materials that exhibit nonlinear behaviors in wave propagation. Thin films con...

In this paper, the nonparaxial nonlinear Schrödinger (NNLS) equation by considering its integrability which enables the propagation of ultra-broad nonparaxial beams in a planar optical waveguide is studied. The plenty numbers of solitary wave solutions by using Hirota’s bilinear scheme are found, in addition, the bilinear transformation and also th...

In this paper, the Gilson–Pickering (GP) equation with applications for wave propagation in plasma physics and crystal lattice theory is studied. The model with wave propagation in plasma physics and crystal lattice theory is explained. A collection of evolution equations from this model, containing the Fornberg–Whitham, Rosenau–Hyman, and Fuchsste...

The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a known equation. To achieve this, an illustrative example of the VC generalized shallow water wave equation is provided to demonstrate the feasibility and reliability of the used procedure in this study. It is shown that Hirota...

In this paper, the Gilson–Pickering equation is studied which enables a wave propagation in plasma physics and crystal lattice theory. Based on the auxiliary transformations, some sets of the nonlinear form of ODE along with some analytic solutions are derived. To study the characterizations of the new waves, the crystal lattice theory and plasma p...

In this paper, we study the cubic–quintic nonlinear Helmholtz equation which enables a pulse propagating with Kerr-like and quintic properties further spatial dispersion. By noticing that the system is a nonintegrable one, we could get variety forms of solitary wave solutions by using a generalized G′∕G-expansion method. In particular, we investiga...

In this article, we investigate the generalized (2+1)-dimensional shallow water wave equation which enables an unidirectional propagation of shallow-water waves. By noticing that the system is integrable, we could get the diverse forms of the solitary wave solutions by using the rogue wave and semi-inverse variational principle (SIVP) schemes. In p...

In this paper, the exact soliton solutions and other exact solutions for nonlinear Schrodinger’s equation having Kudryashov’s quintuple power law of refractive index together with dual form of generalized nonlocal nonlinearity are studied. By noticing that the system is a non-integrable one, the diverse of solitary wave solutions by using a general...

In this paper, we investigate the (3+1)-dimensional Burger system which is employed in soliton theory and generated by considering the Hirota bilinear equation. We conclude some novel analytical solutions, including 2-lump-type, interaction between 2-lump and one kink, two lump and two kink of type I, two lump and two kink of type II, two lump and...

In this paper, we get certain the lump-trigonometric solutions and rogue waves with predictability of a (2+1)-dimensional Konopelchenko–Dubrovsky equation in fluid dynamics with the assistance of Maple based on the Hirota bilinear form. We first construct a general quadratic form to get the general lump solution for the referred model. At the same...

In this paper, we got a novel kind of rogue waves with the predictability of (2 + 1)-dimensional nonlocal Gardner equation with the aid of Maple according to the Hirota bilinear model. We first construct a general quadratic function to derive the general lump solution for the mentioned equation. At the same time, the lumpoff solutions are demonstra...

In this paper, the exact analytical solutions to the generalized Schrödinger equation are investigated. The Schrodinger type equations bearing nonlinearity are the important models that flourished with the wide-ranging arena concerning plasma physics, nonlinear optics, fluid-flow, and the theory of deep-water waves, etc. In this exploration, the so...

This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method. The obtained new results are defined in the styles of the exponential and rational functions. The derived new soliton structures are stable, serviceable, and f...

In this paper, the (3+1)-dimensional variable-coefficient generalized nonlinear wave equation arising in a liquid with gas bubbles is studied. The Hirota bilinear technique and binary bell polynomials are considered. Some new analytic solutions containing one-lump soliton, two-lump soliton, and three-lump soliton, and also 1-breather and 1-lump, th...

In this article, the new exact solitary wave solutions for the generalized nonlinear Schrödinger equation with parabolic nonlinear (NL) law employing the improved tanh(Γ(ϖ))-coth(Γ(ϖ)) function technique and the combined tan(Γ(ϖ))-cot(Γ(ϖ)) function technique are obtained. The offered techniques are novel and also for the first time in this study a...

In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rational solutions by selecting the interaction between a lump and one- or two-soliton solutions are obt...

This article investigates the extended homoclinic (heteroclinic) breather wave solutions and interaction periodic and dark soliton solutions to the nonlinear vibration and dispersive wave systems. The solutions include periodic, breather, and soliton solutions. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize...

In this paper, the numerical solutions are proposed for the 1D Benjamin–Bona–Mahony (BBM) equation and 2D coupled BBM system by using Galerkin finite element technique. In this regard, the cubic B-splines and linear triangular elements are used, respectively. In 1D space, a proposed numerical scheme is implemented to a test problem including the mo...

In this paper, the novel exact solitary wave solutions for the generalized nonlinear Schr¨odinger equation with parabolic nonlinear (NL) law employing the improved cosh(Γ(ϖ))-sech(Γ(ϖ)) function scheme and the combined cos(Γ(ϖ))-sec(Γ(ϖ)) function scheme are found. Diverse collections of hyperbolic and trigonometric function solutions acquired re...

In this paper, the novel exact solitary wave solutions for the generalized nonlinear Schr¨odinger equation with parabolic nonlinear (NL) law employing the improved cosh(Γ($))-sech(Γ($)) function scheme and the combined cos(Γ($))-sec(Γ($)) function scheme are found. Diverse collections of hyperbolic and trigonometric function solutions acquired rely...

The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in t...

The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in t...

This paper investigates the cross-kink and solitary wave solutions to the nonlinear vibration and dispersive wave systems. The solutions include periodic, cross-kink, and solitary wave solutions. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize the Cole-Hopf algorithm to get the exact solutions of the (2+1)-di...

This paper investigates the combined damped sinusoidal oscillation solutions to the 3 + 1 -D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of...

In this research, the (2 + 1)-dimensional (D) variable-coefficient (VC) Caudrey–Dodd–Gibbon–Kotera–Sawada model used in the soliton hypothesis and implemented by operating the Hirota bilinear scheme is studied. A few modern exact analytical outcomes containing interaction between a lump-two kink soliton, interaction between two-lump, the interactio...

In this research, the (2 + 1)-dimensional (D) variable-coefficient (VC) Caudrey–Dodd–Gibbon–Kotera–Sawada model used in soliton hypothesis and implemented by operating the Hirota bilinear scheme is studied. A few modern exact analytical outcomes containing interaction between a lump-two kink soliton, interaction between two-lump, the interaction be...

Here, the miscellaneous soliton solutions of the generalized nonlinear Schrödinger equation are considered that describe the model of few-cycle pulse propagation in metamaterials with parabolic law of nonlinearity. The novel analytical wave solutions to the mentioned nonlinear equation in the sense of the nonlinear ordinary differential transform e...

In this work, we study the generalized (2+1)-dimensional Hietarinta equation by utilizing Hi- rota's bilinear method. In addition, the lump solution and breather solution are presented. Using suitable mathematical assumptions, the new types of lump, singular, and breather soliton solutions are derived and established in view of the hyperbolic, trig...

We develop L1-norm model assuming that is always feasible and bounded for ranking extreme efficient decision making units (DMUs) in stochastic data envelopment analysis (DEA). And also, we present a deterministic equivalent of stochastic model. It is shown that this deterministic model can be convert to a quadratic program. Finally, the proposed mo...

In the current work, the modified (2 + 1)-dimensional Hietarinta model is considered by employing Hirota's bilinear scheme. Likewise, the bilinear formalism is obtained for the considered model. In addition, the periodic-solitary, periodic wave, cross-kink wave, and interaction between stripe and periodic wave solutions of the mentioned equation by...

This current research is considered some new exact soliton solutions to the time-fractional three coupled non-linear Maccari's system in complex form with novel truncated M-fractional derivative. The obtained results may be used in the description of the model in fruitful way. The novel derivative operator is applied to study the aforementioned mod...

To explain the magneto-optical (MO) data in GaAs/InAs/GaAs/MgO/Co/Au thin-film structures, we modeled the optical interactions within magnetic layered structures. Firstly, for a numerical simulation of the MO effects, a full matrix model based on Yeh's formalism is employed, and secondly for the comparison between different magnetic and non-magneti...

In this article, we study the generalized (3+1)-dimensional nonlinear wave equation where is investigated in soliton theory and by employing the Hirota’s bilinear method the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, some Lump solutions, Lump-kink solutions, Lump-two kink solutions, Lump-periodic solutions,...

In this paper, we check and scan the (3+1)-dimensional variable-coefficient nonlinear wave equation which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including cross-kink soliton solutions, breather wave solutions, interaction between stripe and perio...

This paper aims to compute solitary wave solutions and soliton wave solutions based on the ansatz methods to the perturbed nonlinear Schrödinger equation (NLSE) arising in nano-fibers. The improved tan(θ/2)-expansion method and the rational extended sinh–Gordon equation expansion method are used for the first time to obtain the new optical solitons...

In this paper, we study the (3+1)-dimensional variable-coefficient nonlinear wave equation which is taken in soliton theory and generated by utilizing the Hirota bilinear technique. We obtain some new exact analytical solutions, containing interaction between a lump-two kink solitons, interaction between two lumps, and interaction between two lumps...

The Hirota bilinear method is prepared for searching the diverse soliton solutions to the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. Also, the Hirota bilinear method is used to find the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and one-kink soliton solution...

Here, two applicable methods, namely, the tanθ/2-expansion technique and modified exp−θξ-expansion technique are being applied on the time-fractional coupled Jaulent–Miodek equation. Materials such as photovoltaic-photorefractive, polymer, and organic contain spatial solitons and optical nonlinearities, which can be identified by seeking from energ...

In the current study, an analytical treatment is studied starting from the 2+1-dimensional generalized Hirota-Satsuma-Ito (HSI) equation. Based on the equation, we first establish the evolution equation and obtain rational function solutions by means of the bilinear form with the help of the Hirota bilinear operator. Then, by the suggested method,...

This paper deals with cross-kink waves in the (2+1)-dimensional KP–BBM equation in the incompressible fluid. Based on Hirota’s bilinear technique, cross-kink solutions related to KP–BBM equation are constructed. Taking the special reduction, the exact expression of different types of solutions comprising exponential, trigonometric and hyperbolic fu...

Introduction The multiple Exp-function scheme is employed for searching the multiple soliton solutions for the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation. Objectives Moreover, the Hirota bilinear technique is utilized to detecting the lump and interaction with two stripe soliton solutions. Methods...

In this paper, we study a new generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko equation which is considered in soliton theory and generated by considering the Hirota trilinear operators. We retrieve some novel exact analytical solutions, including lump-type wave, breather wave as well as breather-kink-type wave, and lump-kink wave solution...