Darboux transformation and soliton solutions for the (2+1)-dimensional nonlinear Schrödinger hierarchy with symbolic computation

Hai-Qiang Zhang, Bo Tian, Li-Li Li and Yu-Shan Xue

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 1, 9-20

Abstract: In this paper, the N-fold Darboux transformation is applied to the Lax pair associated with the (2+1)-dimensional nonlinear Schrödinger hierarchy. The general explicit formula for N-soliton solution is derived in terms of Vandermonde-like determinant expression. On the zero background, two different families of soliton solutions (multi-line soliton and multi-parabola soliton solutions) are constructed by applying the Darboux transformation successively. Based on the figures for several sample solutions, the soliton interactions are discussed by virtue of the physical parameters (amplitude, velocity and direction) of the interacting solitons.

Keywords: (2+1)-dimensional nonlinear Schrödinger hierarchy; Darboux transformation; Soliton; Symbolic computation (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:1:p:9-20

DOI: 10.1016/j.physa.2008.09.032

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