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

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.