Symmetry reductions and rational non-traveling wave solutions for the (2+1)-D Ablowitz-Kaup-Newell-Segur equation. Issue 8 (7th November 2016)

• Record Type: Journal Article
• Authors: Kang, Xiao-rong; Daquan, Xian
• Is Part Of: International journal of numerical methods for heat & fluid flow. Volume 26:Issue 8(2016)
• Page Start: 2331
• Page End: 2339
• Publication Date: 2016-11-07
• Subjects: Exp-function method -- AKNS equation -- Lie symmetric method -- Non-traveling wave solutions -- Rational function method; Heat -- Transmission -- Mathematics -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 536.2
• DOI: 10.1108/HFF-05-2015-0204
• Languages: English
• ISSNs: 0961-5539

Abstract

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.