中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110306-110306.doi: 10.1088/1674-1056/22/11/110306

• GENERAL • 上一篇    下一篇

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

陈俊超a, 李彪b, 陈勇a   

  1. a Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
    b Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China
  • 收稿日期:2013-03-16 修回日期:2013-04-24 出版日期:2013-09-28 发布日期:2013-09-28
  • 基金资助:
    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).

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

Chen Jun-Chao (陈俊超)a, Li Biao (李彪)b, Chen Yong (陈勇)a   

  1. a Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
    b Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China
  • Received:2013-03-16 Revised:2013-04-24 Online:2013-09-28 Published:2013-09-28
  • Contact: Chen Yong E-mail:ychen@sei.ecnu.edu.cn
  • Supported by:
    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).

摘要: 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.

关键词: coupled dynamical nonlinear Schrödinger equations, coupled nonlinear Schrödinger equations with time–space modulation, exact solutions

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.

Key words: coupled dynamical nonlinear Schrödinger equations, coupled nonlinear Schrödinger equations with time–space modulation, exact solutions

中图分类号: 

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