Abstract
In this present work, the simplest equation method is used to construct exact solutions of the DS-I and DS-II equations. The simplest equation method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to nonintegrable equations as well as to integrable ones.
Highlights
IntroductionIn 1996, Ma and Fuchssteiner proposed a powerful approach for finding exact solutions to nonlinear differential equations [18]
In this paper, we consider the Davey–Stewartson (DS) equations [1,2,3] iqt +1 δ2 2 qxx + δ2qyy+ λ|q|2q − φxq = 0, (1)φxx − δ2φyy − 2λ |q|2 x = 0.c Vilnius University, 2012The case δ = 1 is called the DS-I equation, while δ = i is the DS-II equation
The Davey–Stewartson equations are reduced to Hamiltonian ODEs [4], and so exact solutions could be furnished by the integrability [5] of finite-dimensional Hamiltonian systems
Summary
In 1996, Ma and Fuchssteiner proposed a powerful approach for finding exact solutions to nonlinear differential equations [18]. Their key idea is to expand solutions of given differential equations as functions of solutions of solvable differential equations, in particular, polynomial and rational functions. The simplest equation method is a very powerful mathematical technique for finding exact solutions of nonlinear ordinary differential equations. It has been developed by Kudryashov [6,7,8,9,10] and used successfully by many authors for finding exact solutions of ODEs in mathematical physics [20, 21].
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