Periodic solutions of nonlinear Schr?dinger type equations

doi:10.1088/1009-1963/13/6/004

中国物理B ›› 2004, Vol. 13 ›› Issue (6): 805-810.doi: 10.1088/1009-1963/13/6/004

Periodic solutions of nonlinear Schr?dinger type equations

范天佑¹, 刘官厅²

(1)Department of Physics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Physics, Beijing Institute of Technology, Beijing 100081, China; Department of Mathematics, Inner Mongolia Normal University, Huhhot 010022, China

收稿日期:2003-10-08 修回日期:2003-11-03 出版日期:2004-07-05 发布日期:2005-07-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10372016), the Inner Mongolia Natural Science Foundation (Grant No 200308020101) and the Key Programme of Scientific Research Foundation for Youth of Inner Mongolia Normal Uni

Periodic solutions of nonlinear Schrödinger type equations

Liu Guan-Ting (刘官厅)^ab, Fan Tian-You (范天佑)^a

^a Department of Physics, Beijing Institute of Technology, Beijing 100081, China; ^b Department of Mathematics, Inner Mongolia Normal University, Huhhot 010022, China

Received:2003-10-08 Revised:2003-11-03 Online:2004-07-05 Published:2005-07-05
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10372016), the Inner Mongolia Natural Science Foundation (Grant No 200308020101) and the Key Programme of Scientific Research Foundation for Youth of Inner Mongolia Normal Uni

摘要/Abstract

摘要： By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schr?dinger type equations. It is shown that many exact periodic solutions of some nonlinear Schr?dinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions.

Abstract: By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrödinger type equations. It is shown that many exact periodic solutions of some nonlinear Schrödinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions.

Key words: auxiliary equation method, Schrödinger type equation, periodic solution, symbolic computation

中图分类号: (Function theory, analysis)

02.30.-f

03.65.Ge (Solutions of wave equations: bound states)

刘官厅, 范天佑. Periodic solutions of nonlinear Schr?dinger type equations[J]. 中国物理B, 2004, 13(6): 805-810.

Liu Guan-Ting (刘官厅), Fan Tian-You (范天佑). Periodic solutions of nonlinear Schrödinger type equations[J]. Chinese Physics, 2004, 13(6): 805-810.

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Periodic solutions of nonlinear Schr?dinger type equations

Periodic solutions of nonlinear Schrödinger type equations

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