Abstract
In this paper, modified extended tanh method is used to construct more general exact solutions of a (2+1)-dimensional nonlinear Schrödinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and so on and their images.
Highlights
It is well known that Schrödinger equation is one of the most basic equations of quantum mechanics
As it is a powerful tool for solving non relativistic problems in atomic physics, it was widely used in the fields of atomic, molecular, solid state physics, nuclear physics, chemistry and so on
In the past several decades, much efforts have been on this aspect and many useful methods have been proposed such as inverse scattering method, Jacobi elliptic function method, F-expansion method, Darboux transform, the sine-cosine method and the tanh method
Summary
It is well known that Schrödinger equation is one of the most basic equations of quantum mechanics. It reflects the state of micro particle changing with time. Fan has proposed an extended tanh method and obtained the travelling wave solutions that cannot be obtained by the tanh method. Based on this approach, we employed the modified extended tanh method to construct a series of exact travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger (NLS) equation as iut + αuxx + βu yy + r u2 u = 0
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