中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100507-100507.doi: 10.1088/1674-1056/22/10/100507

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Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

曹瑞a b, 张健a   

  1. a College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China;
    b Department of Mathematics, Heze University, Heze 274000, China
  • 收稿日期:2012-12-24 修回日期:2013-04-18 出版日期:2013-08-30 发布日期:2013-08-30
  • 基金资助:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 11071177).

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

Cao Rui (曹瑞)a b, Zhang Jian (张健)a   

  1. a College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China;
    b Department of Mathematics, Heze University, Heze 274000, China
  • Received:2012-12-24 Revised:2013-04-18 Online:2013-08-30 Published:2013-08-30
  • Contact: Cao Rui E-mail:ruicao999@126.com
  • Supported by:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 11071177).

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摘要： In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions.

关键词: generalized nonlinear Schrö, dinger equation, exact solution, trial function method

Abstract: In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions.

Key words: generalized nonlinear Schrödinger equation, exact solution, trial function method

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations) 02.30.Hq (Ordinary differential equations)