Further investigations to extract abundant new exact traveling wave solutions of some NLEEs

In this study,we implement the generalized(G/G)-expansion method established by Wang et al.to examine wave solutions to some nonlinear evolution equations.The method,known as the double(G/G,1/G)-expansion method is used to establish abundant new and further general exact wave solutions to the(3+1)-dimensional Jimbo-Miwa equation,the(3+1)-dimensional Kadomtsev-Petviashvili equation and symmetric regularized long wave equation.The solutions are extracted in terms of hyperbolic function,trigonometric function and rational function.The solitary wave solutions are constructed from the obtained traveling wave solutions if the parameters received some definite values.Graphs of the solutions are also depicted to describe the phenomena apparently and the shapes of the obtained solutions are singular periodic,anti-kink,singular soliton,singular anti-bell shape,compaction etc.This method is straightforward,compact and reliable and gives huge new closed form traveling wave solutions of nonlinear evolution equations in ocean engineering.

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

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 equation.In this work,we effectively derive abundant closed form wave solutions of these equations by using the double(G′/G,1/G)-expansion method.The obtained solutions include singular kink shaped soliton solutions,periodic solution,singular periodic solution,single soliton and other solutions as well.We 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.

New applications of the two variable (G ′/ G,1/ G)-expansion method for closed form traveling wave solutions of integro-differential equations

Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions of nonlinear evolution equations.In our research,we ascertain abundant new closed form traveling wave solution of the nonlinear integro-differential equations via Ito equation,integro-differential Sawada-Kotera equation,first integro-differential KP hierarchy equation and second integro-differential KP hierarchy equation by two variable(G/G,1/G)-expansion method with the help of computer package like Mathematica.Some shape of solutions like,bell profile solution,anti-king profile solution,soliton profile solution,periodic profile solution etc.are obtain in this investigation.Trigonometric function solution,hyperbolic function solution and rational function solution are established by using our eminent method and comparing with our results to all of the well-known results which are given in the literature.By means of free parameters,plentiful solitary solutions are derived from the exact traveling wave solutions.The method can be easier and more applicable to investigate such type of nonlinear evolution models.

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

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 Mathematica.Three functions and the rational functions solution are found.The method demonstrates power,reliability and efficiency.Indeed,the method is the generalization of the well-known(G/G)-expansion method established by Wang et al.and the method also presents a wider applicability for conducting nonlinear wave equations.