Symmetry reductions and rational non-traveling wave solutions for the (2+1)-D Ablowitz-Kaup-Newell-Segur equation

Abstract

Purpose

The purpose of this paper is to find out some new rational non-traveling wave solutions and to study localized structures for (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation.

Design/methodology/approach

Along with some special transformations, the Lie group method and the rational function method are applied to the (2+1)-dimensional AKNS equation.

Findings

Some new non-traveling wave solutions are obtained, including generalized rational solutions with two arbitrary functions of time variable.

Research limitations/implications

As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.

Originality/value

With the help of the Lie group method, special transformations and the rational function method, new non-traveling wave solutions are derived for the AKNS equation by Maple software. These results are much useful for investigating some new localized structures and the interaction of waves in high-dimensional models, and enrich dynamical features of solutions for the higher dimensional systems.

Citation

Kang, X.-r. and Daquan, X. (2016), "Symmetry reductions and rational non-traveling wave solutions for the (2+1)-D Ablowitz-Kaup-Newell-Segur equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2331-2339. https://doi.org/10.1108/HFF-05-2015-0204