Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation

doi:10.1088/1674-1056/22/11/110306

Abstract We construct various novel exact solutions of two coupled dynamical nonlinear Schrödinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrödinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrödinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.

Keywords: coupled dynamical nonlinear Schrödinger equations coupled nonlinear Schrödinger equations with time–space modulation exact solutions

Received: 16 March 2013
Revised: 24 April 2013
Accepted manuscript online:

PACS:	03.75.-b
	05.45.Yv	(Solitons)
	31.15.-p	(Calculations and mathematical techniques in atomic and molecular physics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11275072, 11075055, and 11271211), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), the Shanghai Leading Academic Discipline Project, China (Grant No. B412), the National High Technology Research and Development Program of China (Grant No. 2011AA010101), and the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213).

Corresponding Authors: Chen Yong
E-mail: ychen@sei.ecnu.edu.cn

Cite this article:

Chen Jun-Chao (陈俊超), Li Biao (李彪), Chen Yong (陈勇) Novel exact solutions of coupled nonlinear Schrödinger equations with time–space modulation 2013 Chin. Phys. B 22 110306

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