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.
Along with some special transformations, the Lie group method and the rational function method are applied to the (2+1)-dimensional AKNS equation.
Some new non-traveling wave solutions are obtained, including generalized rational solutions with two arbitrary functions of time variable.
As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.
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.
This work was supported by National Natural Science Foundation of China under Grant No. 11204250, No. 11202175 and No. 11361048.
Kang, X. 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-05-2015-0204Download as .RIS
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