The simplest equation method and its application for solving the nonlinear NLSE, KGZ, GDS, DS, and GZ equations. (English) Zbl 1397.35069

Summary: A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.


35G20 Nonlinear higher-order PDEs
35C05 Solutions to PDEs in closed form
35Q55 NLS equations (nonlinear Schrödinger equations)
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