广西师范大学学报（自然科学版） ›› 2013, Vol. 31 ›› Issue (4): 71-77.

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五阶饱和非线性薛定谔方程的多辛方法

蒋朝龙, 罗婷, 孙建强   

  1. 海南大学信息科学技术学院,海南海口570228
  • 收稿日期:2013-04-26 出版日期:2013-12-20 发布日期:2018-11-26
  • 通讯作者: 孙建强(1971—),男,湖南双峰人,海南大学教授,博士。E-mail:sunjq123@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11161017);海南大学科研启动基金资助项目(kyqd1053)

Multi-symplectic Method of the Fifth Order Saturated Nonlinear Schrödinger Equation

JIANG Chao-long, LUO Ting, SUN Jian-qiang   

  1. College of Information Science and Technology,Hainan University,Haikou Hainan 570228,China
  • Received:2013-04-26 Online:2013-12-20 Published:2018-11-26

摘要： 本文将五阶饱和非线性薛定谔方程转化成多辛结构,利用中点Preissman格式进行离散,得到其多辛格式及相应的守恒律。利用多辛格式对不同的非线性饱和效应和振辐差下的孤立波进行数值模拟,数值结果表明:多辛格式能很好地模拟光孤子行为并近似保持能量守恒特性,非线性饱和效应和振幅对孤立波的传输有很大的影响,孤立子碰撞会导致系统的能量发生显著地变化。

关键词: 五阶饱和非线性薛定谔方程, 多辛算法, 孤立子波

Abstract: The fifth order saturated nonlinear Schrödinger equation is transformed into the multi-symplecticstructure and discretizated by the middle Preissman scheme.The multi-symplectic scheme and the corresponding multi-symplectic conservation is obtained.The solitary waves with different nonlinear saturated effects and different amplitude are simulated by the multi-symplectic scheme.Numerical results show the multi-symplectic scheme can well simulate the behaviors of optical solitons and approximately preserve the energy conservation property.Nonlinear saturated effects and the amplitude have obvious effect on the propagation of the solitary waves and the collision of the solitary waves also have obvious effect on the change of the system energy.

Key words: fifth order saturated nonlinear Schrö, dinger equation, multi-symplectic method, solitary wave

中图分类号: 

  • O241.82
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