Dark solitons, Lax pair and infinitely-many conservation laws for a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in the inhomogeneous Heisenberg ferromagnetic spin chain

Author:

Zhao Xue-Hui1,Tian Bo23,Liu De-Yin23,Wu Xiao-Yu23,Chai Jun23,Guo Yong-Jiang12

Affiliation:

1. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China

2. School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China

3. State Key Laboratory of Information Photonics and Optical Communications, Beijing 100876, China

Abstract

Under investigation in this paper is a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain. Lax pair and infinitely-many conservation laws are derived, indicating the existence of the multi-soliton solutions for such an equation. Via the Hirota method with an auxiliary function, bilinear forms, dark one-, two- and three-soliton solutions are derived. Propagation and interactions for the dark solitons are illustrated graphically: Velocity of the solitons is linearly related to the coefficients of the second- and fourth-order dispersion terms, while amplitude of the solitons does not depend on them. Interactions between the two solitons are shown to be elastic, while those among the three solitons are pairwise elastic.

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

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