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Wave profile analysis of a couple of(3+1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach

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Journal of Ocean Engineering and Science 2022年第3期7卷 272-279页

作者： md.Rezwan Ahamed Fahim Purobi Rani Kundu md.Ekramul Islam m.ali akbar m.S.Osman Department of mathematics Pabna University of Science and TechnologyBangladesh Department of Applied mathematics University of RajshahiBangladesh Department of mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt Department of mathematics Faculty of Applied ScienceUmm Alqura UniversityMakkah 21955Saudi Arabia

The(3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation,dynamics of shallow water wave,plasma fluid model,chemical kinematics,chemical engineering,geochemistry,and many other *** this article,we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in *** a result,wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations,containing kink,breather soliton,bell-shaped soliton,and periodic *** extract the soliton solutions of the high-dimensional nonlinear evolution equations,a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions *** sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear *** study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension(HNEEs).Closed-form solutions are carefully illustrated and discussed through diagrams.

关键词： Sine-Gordon expansion approach Kadomtsev-Petviashvili equation modified KdV-Zakharov-Kuznetsov equation soliton solutions

Generalized and Improved(G′/G)-Expansion method Combined with Jacobi Elliptic Equation

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Communications in Theoretical Physics 2014年第6期61卷 669-676页

作者： m.ali akbar Norhashidah Hj.mohd.ali E.m.E.Zayed School of mathematical Sciences Universiti Sains Malaysia Department of Applied mathematics University of Rajshahi mathematics Department Faculty of Science Zagazig University

In this article, we propose an alternative approach of the generalized and improved(G′/G)-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti–Leon–Pempinelle equation, the Pochhammer–Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacobi elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations.

关键词： Jacobi椭圆方程展开法非线性发展方程 Burgers方程广义二阶线性方程自由参数孤立波解

Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion method

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Communications in Theoretical Physics 2012年第2期57卷 173-178页

作者： m.ali akbar Norhashidah Hj.mohd.ali E.m.E.Zayed School of mathematical Sciences Universiti Sains MalaysiaMalaysia mathematics Department Faculty of ScienceZagazig UniversityZagazigEgypt

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.

关键词：行波解展开法解方程布雷广义自由参数三角函数有理函数

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational(G'/G)-expansion method

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Journal of Ocean Engineering and Science 2018年第1期3卷 76-81页

作者： Tarikul Islam m.ali akbar Abul Kalam Azad Department of mathematics Hajee Mohammad Danesh Science and Technology UniversityDinajpurBangladesh Department of Applied mathematics Rajshahi UniversityRajshahiBangladesh

In this article,the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regu-larized long wave(SRLW)equation are successfully examined by the recently established rational(G/G)-expansion *** suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex ***,the theories of the ordinary differential equations are implemented *** types closed form traveling wave solutions,such as hyper-bolic function,trigonometric function and rational,are constructed by using the suggested method in the sense of conformable fractional *** obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a *** is observed that the performance of the rational(G/G)-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

关键词： Nonlinear space-time fractional equations Nonlinear fractional complex transformation Conformable fractional derivative Exact solutions

Study of abundant explicit wave solutions of the Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation and the shallow water wave equation

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Propulsion and Power Research 2018年第4期7卷 320-328页

作者： H.m.Shahadat ali m.mamun miah m.ali akbar Department of Applied mathematics Noakhali Science and Technology UniversityNoakhali 3814Bangladesh Department of mathematics Khulna University of Engineering&Technology.Khulna 9203Bangladesh Department of Applied mathematics University of Rajshahi.Rajshahi 6205Bangladesh

In this article,the two variable(G'G,1/G)-expansion method is suggested to investigate new and further general multiple exact wave solutions to the Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation and the shallow water wave equation which arise in mathematical physics with the aid of computer algebra software,like *** functions and the rational functions solution are *** method demonstrates power,reliability and ***,the method is the generalization of the well-known(G/G)-expansion method established by Wang et *** the method also presents a wider applicability for conducting nonlinear wave equations.

关键词： Explicit wave solutions Computer algebra software Drinfeld-Sokolov-Satsuma-Hirota(DSSH)equation Shallow water wave equation Soliton

Abundant general solitary wave solutions to the family of KdV type equations

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Journal of Ocean Engineering and Science 2017年第1期2卷 47-54页

作者： md.Azmol Huda m.ali akbar Shewli Shamim Shanta mathematics Discipline Khulna UniversityKhulnaBangladesh Department of Applied mathematics University of RajshahiRajshahiBangladesh Department of mathematics University of RajshahiRajshahiBangladesh

This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations(NLEEs)through the application of the(G/G,1/G)-expansion *** method is allied to the widely used(G/G)-method initiated by Wang et *** can be considered as an extension of the(G/G)-expansion *** effectiveness,the method is applied to the family of KdV type *** general form solitary wave solutions as well as periodic solutions are successfully obtained through this ***,in the obtained wider set of solutions,if we set special values of the parameters,some previously known solutions are *** approach of this method is simple and elegantly *** been computerized it is also powerful,reliable and effective.

关键词： Nonlinear evolution equation Solitary wave solution Potential KdV equation Complex modified KdV equation

The new types of wave solutions of the Burger’s equation and the Benjamin-Bona-mahony equation

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Journal of Ocean Engineering and Science 2018年第1期3卷 1-10页

作者： md.Azmol Huda m.ali akbar Shewli Shamim Shanta mathematics Discipline Khulna UniversityBangladesh Department of Applied mathematics University of RajshahiBangladesh Department of mathematics University of RajshahiBangladesh

In this article,we suggest the two variable(G/G,1/G)-expansion method for extracting further general closed form wave solutions of two important nonlinear evolution equations(NLEEs)that model one-dimensional internal waves in deep water and the long surface gravity waves of small amplitude propagating *** method can be regarded as an extension of the(G/G)-expansion *** ansatz of this extension method to obtain the solution is based on homogeneous balance between the highest order dispersion terms and nonlinearity which is similar to the(G/G)method whereas the auxiliary linear ordinary differential equation(LODE)and polynomial solution *** applied this method to find explicit form solutions to the Burger’s and Benjamin-Bona-mahony(BBm)equations to examine the effectiveness of the method and tested through mathematical computational software *** new exact travelling wave solutions in more general form of these two nonlinear equations are derived by this extended *** method introduced here appears to be easier and faster comparatively by means of symbolic computation system.

关键词： Travelling wave solution Soliton Burger’s equation Benjamin-Bona-mahony equation.

A study on the compatibility of the generalized Kudryashov method to determine wave solutions

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Propulsion and Power Research 2021年第1期10卷 95-105页

作者： Hemonta Kumar Barman md.Ekramul Islam m.ali akbar Department of Applied mathematics University of RajshahiRajshahi6205Bangladesh Department of mathematics Pabna University of Science and TechnologyPabna6600Bangladesh

In this article,we establish solitary wave solutions to the Estevez-mansfieldClarkson(EmC)equation and the coupled sine-Gordon equations which are model equations to analyze the formation of shapes in liquid drops,surfaces of negative constant curvature,*** contriving the generalized Kudryashov *** extracted results introduce several types’solitary waves,such as the kink soliton,bell-shape soliton,compacton,singular soliton,peakon and other sort of soliton for distinct valuation of the unknown *** achieved analytic solutions are interpreted in details and their 2D and 3D graphs are *** obtained solutions and the physical structures explain the soliton phenomenon and reproduce the dynamic properties of the front of the travelling wave deformation generated in the dispersive *** shows that the generalized Kudryashov method is powerful,compatible and might be used in further works to found novel solutions for other types of nonlinear evolution equations ascending in physical science and engineering.

关键词： The nonlinear evolution equations(NLEEs) The Estevez-mansfieldClarkson(EmC)equation The coupled sineGordon equations The generalized Kudryashov method Solitons Analytic solutions

Abundant closed form wave solutions to some nonlinear evolution equations in mathematical physics

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Journal of Ocean Engineering and Science 2020年第3期5卷 269-278页

作者： m.mamun miah Aly R.Seadawy H.m.Shahadat ali m.ali akbar Department of mathematics Khulna University of Engineering&TechnologyBangladesh mathematics Department Taibah UniversityAl-Madinah Al-MunawarahSaudi Arabia Department of mathematics Beni-Suef UniversityEgypt Department of Applied mathematics Noakhali Science and Technology UniversityBangladesh Department of Applied mathematics University of RajshahiRajshahi 6205Bangladesh

The propagation of waves in dispersive media,liquid flow containing gas bubbles,fluid flow in elastic tubes,oceans and gravity waves in a smaller domain,spatio-temporal rescaling of the nonlinear wave motion are delineated by the compound Korteweg-de Vries(KdV)-Burgers equation,the(2+1)-dimensional maccari system and the generalized shallow water wave *** this work,we effectively derive abundant closed form wave solutions of these equations by using the double(G′/G,1/G)-expansion *** obtained solutions include singular kink shaped soliton solutions,periodic solution,singular periodic solution,single soliton and other solutions as *** show that the double(G′/G,1/G)-expansion method is an efficient and powerful method to examine nonlinear evolution equations(NLEEs)in mathematical physics and scientific application.

关键词： Close form solutions KdV-Burgers equation The(2+1)-dimensional maccari system The generalized shallow water wave equation