The Modified (G'/G)-expansion Method And Its Appllication

As we all know,nonlinear partial differential equations(NLPDEs) are a vital tool in characterizing many complicated physical phenomena.Hence the investigation of the exact solutions for these NLPDEs becomes more and more important.Exact solutions,especially travelling solutions,can explain many phenomena,such as ones in fluid mechanics,plasma physics,optical fibers,solid state physics and chemical physics.However,because of the complexity of nonlinear partial differential equations and the limitations of mathematics methods,it is difficult to get the exact solutions for all the problems.Therefore,with the help of computerized symbolic computation,much work has been focused on the various extensions and applications of the known algebraic methods to construct the solutions to NLPDEs.Firstly,we modified the(G'/G)-expansion method,to add negative index to the method of the constructive solution of equations,such that more various solutions are obtained. Furthermore,the modified(G'/G)-expansion method is applied to Whitham-Broer-Kaup Like Equations for the first time and we get lots of rich families exact solutions of it.Secondly,in order to find more solutions,based on the homogenous balance method,a new constructive form of solutions with variable coefficient is put forward,by introducing more arbitrary parameter's transformation:ζ=θ(x,y,t),whereθ(x,y,t) is arbitrary function of x,y,t.For a given equation,we get hyperbolic function solutions,rational solutions and trigonometric function solutions.With the transformation:ζ=θ(x,y,t)=p(x,t)+q(y) ,the solutions of(2+1)-dimensional dispersive long wave equation are explicit obtained.