S. M. Rayhanul Islam

Pabna University of Science and Technology | PUST · Department of Mathematics

The paraxial nonlinear Schrödinger equation finds diverse applications in the fields of nonlinear optics, optical communication systems, plasma physics, and mathematical physics. The outcomes of this research endeavor are directed toward achieving three principal objectives. Query ID="Q2" Text=" Kindly check and confirm whether the corresponding af...

The doubly dispersive (DD) equation finds extensive utility across scientific and engineering domains. It stands as a significant nonlinear physical model elucidating nonlinear wave propagation within the elastic inhomogeneous Murnaghan’s rod (EIMR). With this in mind, we have focused on the integration of the DD model and the modified Khater (MK)...

The (2+1)-dimensional long-wave-shortwave resonance interaction (LWSWRI) equation has extensive applications in various fields of science and engineering. The (2+1)-dimensional LWSWRI equation and two analytical techniques have been considered in this manuscript. These schemes, via the advanced auxiliary equation, improve F-expansion techniques app...

The truncated M-fractional Kuralay (TMFK)-II equation is prevalent in the exploration of specific complex nonlinear wave phenomena. Such types of wave phenomena are more applicable in science and engineering. These equations could potentially provide insights into understanding the intricate dynamics of optical phenomena , encompassing solitons, no...

The wave phenomenon of the 2+1 -dimensional Boiti-Leon-Manna-Pempinelli (BLMP) is an asset for investigating the dynamic behavior of waves in fluid dynamics, water wave mechanics, ocean engineering, and science. In this investigation, the object of the research is to explore abundant explicit traveling wave solutions for the 2+1 -dimensional BLMP e...

In this study, we have been considered the Doubly dispersive equation (DDE) and the advanced auxiliary equation approach (AAEA). Through the wave transformation, this model is effectively converted into an ordinary differential equation. With this in mind, a large number of analytic soliton solutions have been inspected in the form of hyperbolic, t...

In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions....

The primary aim of this investigation is to uncover novel optical soliton solutions (OSSs) and conduct a comprehensive stability analysis of a particular model. The extraction of OSSs is facilitated through two potent techniques: the advanced auxiliary equation and the [Formula: see text]-expansion approaches, both proven to be highly effective in...

Investigate the effects of free parameters, dispersion, and nonlinearity on the obtained travelling wave solutions (TWSs) and discuss the nature of wave profile of the TWSs in the real world. We considered governing nonlinear partial differential equations (NLPDEs). The governing equations are translated into ordinary differential equations (ODEs)...

Investigate the effects of free parameters, dispersion, and nonlinearity on the obtained travelling wave solutions (TWSs) and discuss the nature of wave profile of the TWSs in the real world. We considered governing nonlinear partial differential equations (NLPDEs). The governing equations are translated into ordinary differential equations (ODEs)...

The stochastic chiral nonlinear Schrödinger equation (SCNLSE) is considered and the wave phenomenon of this model is very effective in optical fiber, communication systems and others. Through the wave transformation, this model is effectively converted into an ordinary differential equation. The objective of this investigation is to obtain optical...

In this manuscript, the primary motivation is the implementation of the advanced exp − ð ϕ ξ ð ÞÞ-expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas-Arshed model and the (3 + 1)-dimensional Kadomtsev-Petviashvili equation. Here, the solutions' behaviors are present...

Nonlinear models (NLMs), being an important topic in mathematical physics, have attracted a lot of attention in the international research community because they have numerous uses in human life. These NLMs are typically implemented to illuminate various complicated natural phenomena. NLMs have been seen in fluid mechanics, optical physics, signal...

In this article, we investigated the Landau–Ginzburg–Higgs (LGH) equation, focusing on the analysis of isolated soliton solutions and their stability. To compute the isolated soliton solutions, we used the advanced auxiliary equation (AAE) approach, which has proven to be a powerful and efficient method for extracting soliton solutions in various n...

The Doubly Dispersive Equation (DDE) finds extensive utility across scientific and engineering domains. It stands as a significant nonlinear physical model elucidating nonlinear wave propagation within the elastic inhomogeneous Murnaghan’s rod (EIMR). With this in mind, we have focused on the integration of the DDE model and the advanced auxiliary...

The Chen-Lee -Liu model has many applications in assorted fields, particularly in the study of nonlinear dynamics, chaos theory, circuit design, signal processing, secure communications, encryption and decryption of chaotic signals, as well as cryptography. The modified extended auxiliary equation mapping method has been applied to the Chen-Lee-Liu...

In this research work, two mathematical models, the (1+1)-dimensional cKdV–mKdV equation and the sinh-Gordon (shG) equation, are studied using an analytical method to obtain solitary wave solutions. The paper presents explicit parameterized traveling wave solutions for these equations, with hyperbolic function solutions resulting in solitary wave s...

The Biswas-Arshed (BA) model is an essential wave propagation model in nonlinear optics and optical fibers. In this manuscript, the enhanced G′/G-expansion method is taken into consideration. The BA model is used with this technique to locate visual soliton solutions. The solutions to the hyperbolic and trigonometric functions are determined using...

The two-dimensional nonlinear complex coupled Maccari system is a significant model in optics, quantum mechanics, plasma physics, hydrodynamics and some other fields. In this article, we have investigated scores of broad-spectral soliton solutions to the stated system via the auxiliary equation technique. The obtained solutions are established as a...

In this study, we explain the impacts of nonlinearity and wave dispersion parameters on the soliton pulses of the (2+1)-dimensional Kundu–Mukherjee–Naskar equation (KMNE). In this regard, some new optical solitons are received via the unified method to the aforesaid equation to explain such impacts of the soliton pulses. The presenting optical soli...

In this study, the unified and improved F-expansion methods are applied to derive exact traveling wave solutions of the simplified modified Camassa-Holm (SMCH) equation. The current methods can calculate all branches of solutions at the same time, even if several solutions are quite near and therefore impossible to identify via numerical methods. A...

In this study, the Biswas-Arshed equation (BAE) is handled with the beta time derivative. This model compensates for the group velocity dispersion (GVD) by the dispersion of time and space. Optical soliton and other solutions of BAE are obtained by the modified extended auxiliary equation mapping and improved F-expansion methods. Based on the used...

In this study, we have considered the (2+1)-dimensional paraxial nonlinear Schrödinger (NLS) equation in Kerr media and used the (w/g) -expansion method. The g′ and (g′/g2)-expansion techniques have been customized from the (w/g)-expansion method. We applied these two techniques to the paraxial NLS equation and found the optical soliton solutions....

In plasma physics and water waves, the Gilson-Pickering equation is an important unidirectional wave propagation model. A large number of analytic wave solutions have been established in the form of hyperbolic, trigonometric, exponential, and rational functions using the advanced auxiliary equation approach in this study. The solutions obtained hav...

The one-dimensional long water wave propagation in a nonlinear medium, including the dispersion process, is well simulated by the fractional-order modified equal-width (MEW) equation. This article establishes several recognized, standard, inclusive, and scores of typical exact wave solutions to the MEW equation using the double G'/G,1/G-expansion m...

The Kundu–Mukherjee–Naskar (KMN) model is considered for describing the pulse propagation in optical fibres and communication systems. Two efficient approaches via the exp (−φ(ξ))-expansion and the improved F-expansion schemes are applied to the KMN model and in order to convert the KMN equation to an ODE, we test the complex wave conversions and p...

This manuscript investigates the exact travelling wave solutions of the (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. By employing the unified method, a large amount of new soliton solutions are derived. All soliton solution are trigonometric and hyperbolic function solutions. Based on the obtained solutions, we have discussed...

The solitary dynamics of the Biswas–Arshed (BA) model without self-phase modulation are investigated in the present study. To compensate for the deserted small group velocity dispersion, the BA model includes higher-order spatio-temporal dispersion. The optical soliton solutions of the BA model are examined to use the unified strategy. The solution...

This manuscript employs an exact and explicit soliton solution of the Drinfel'd–Sokolov–Wilson (DSW) equation. The wave phenomena of the obtained solutions are applied to water wave mechanics, fluid dynamics, ocean engineering and science. The new auxiliary equation (NAE) method was not applied to the DSW model. As a result, we applied this model t...

In our manuscript, the (2+1)-dimensional Zakharov-Kuznetsov modified equal width (ZK-MEW) and couple breaking soliton (BS) equations are considered and implemented for the first time using a modified version of the new Kudryashov method (NKM). Based on the suggested way, we will extract analytical soliton solutions of the stated equations. The resu...

The focus of this article is to find the exact traveling wave solutions to Calogero–Bogoyavlenskii–Schiff (CBS) equation by employing the exp−Φζ expansion method. The traveling wave solutions are expressed by the hyperbolic function solutions, trigonometric function solutions and rational function solutions. 3D and 2D charts are drawn from the obta...

In this paper, we obtained the exact solutions of the (1 + 1)-dimensional nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) and the seventh-order Sawada–Kotera–Ito (S-K Ito) equations with the help of the (w/g)-expansion method specially the (g′/g2)-expansion and (g′)-expansion methods. Soliton solutions found for the given equations are i...

The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel analytical solutions such as hyperbolic, trigonometric,...

The new Hamiltonian amplitude (nHA) equation deals with some of the disabilities of the modulation wave-train. The main task of this paper is to extract the analytical wave solutions of the nHA equation. Based on the unified scheme, analytical wave solutions are attained in terms of hyperbolic and trigonometric function solutions. In order to promp...

The new Hamiltonian amplitude (nHA) equation deals with some of the disabilities of the modulation wave-train. The main task of this paper is to extract the analytical wave solutions of the nHA equation. Based on the unified scheme, analytical wave solutions are attained in terms of hyperbolic and trigonometric function solutions. In order to promp...

In this paper, we extract the enormous soliton solutions from the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation with the aid of enhanced (G^'/G)-expansion method in nonlinear dynamics of magnets. All soliton solutions represent as standings of hyperbolic function solution and trigonometric functions solution with arbitrary p...

The present paper applies the exp(−𝜑(𝜉))-expansion and the extended tanh-function methods to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain (HFSC) equation. The applied methods acquire some new exact traveling wave solutions to the HFSC equation, which are representing the hyperbolic, trigonometric,exponential and rational function solut...

In this article, we implement the modified simple equation (MSE) and improve F-expansion method to find the exact solutions of the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chain (HFSC) equation and construct traveling wave solutions in terms of hyperbolic functions, trigonometric functions and rational functions with arbitrary parameters....

The enhanced (G′/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney–Luke equation by using the enhanced (G′/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NL...

In this article, the enhanced (G'/G)-expansion method has been successfully implement to seek travelling wave solutions of the coupled (1+1)-dimensional Broer-Kaup equations, whose equationdescribes the bi-directional propagation of long wave in shallow water. This method is more effective,direct and can be use for solving the nonlinear evolution e...

In this paper, we implement the exp(−Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We o...

In this paper, the enhanced (G G / )-expansion method is used to assemble the traveling wave solutions involving parameters of the Foam Drainage equation, where) ( G G  satisfies a second order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. When some arbitrary...

The enhanced (G′/G)-expansion method is very effective and powerful method to find the exact traveling wave solutions of nonlinear evolution equations. We choose the Phi-4 equation to illustrate the validity and advantages of this method. As a result, many exact traveling wave solutions are obtained, which include soliton, hyperbolic function and t...

In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary wave...

In this article, we construct the traveling wave solutions involving parameters of nonlinear evolutions equations via the Benney-Luke equation using the exp(-Φ(ξ))-expansion method. The traveling wave solutions are expressed in terms of hyperbolic, trigonometric and rational functions. When the parameters are taken special values, the solitary wave...

Bangladesh is frequently cited as one of the country’s most vulnerable to climate change, despite the country’s insignificant contribution to climate change. Any changes in climate will, thus, increase uncertainty regarding rice production as climate is major cause of year-to-year variability in rice productivity. This study analyzed the empirical...

The study examines the trend of three main climatic variables (eg. Temperature, Rainfall and Relative humidity) for Rajshahi, Bangladesh by using the time series data for the 1972-2010 period and assesses the relationship between the variables and the yield of three major rice crops (eg. Aus, Aman and Boro). The results of Ordinary Least Squares (O...

The nonlinear physical model such as the cubic nonlinear Schrodinger equation has been applied in many branches of physics. In this article, the enhanced (G /G)-expansion method is applied to evaluate new exact traveling wave solutions of the complex Schrodinger equation with cubic nonlinearity. The traveling wave solutions are expressed by hyperbo...

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact s...

In this work we study the Gardner equation or the combined KdV-mKdV equation. We use the exp(-Φ(ξ))-expansion method for a reliable treatment to establish exact traveling wave solutions then the solitary wave solutions for the aforementioned nonlinear partial differential equation (NPDEs). As a result, the traveling wave solutions are obtained in f...