华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (4): 42-51.doi: 10.3969/j.issn.1000-5641.2019.04.005

• 数学 • 上一篇    下一篇

双模耦合KdV方程的多孤子解与精确解

赵倩, 白喜瑞   

  1. 宁波大学 数学系, 浙江 宁波 315211
  • 收稿日期:2018-06-28 出版日期:2019-07-25 发布日期:2019-07-18
  • 作者简介:赵倩,女,硕士研究生,研究方向为非线性数学物理.E-mail:15058429092@163.com;白喜瑞,女,硕士研究生,研究方向为偏微分方程.E-mail:15729216969@163.com.
  • 基金资助:
    国家自然科学基金(11471174);宁波市自然科学基金(2014A610018)

Two-mode coupled KdV equation: Multiple-soliton solutions and other exact solutions

ZHAO Qian, BAI Xi-rui   

  1. Department of Mathematics, Ningbo University, Ningbo Zhejiang 315211, China
  • Received:2018-06-28 Online:2019-07-25 Published:2019-07-18

摘要: 根据简化的Hirota双线性方法和Cole-Hopf变换,当一个新的双模耦合KdV方程中的非线性参数与耗散参数取特殊值时,得到了该新的双模耦合KdV方程的多孤子解.同时,当方程中的非线性参数与耗散参数取一般值时,通过不同的函数展开法,如tanh/coth法和Jacobi椭圆函数法,可得到这个方程的其他精确解.

关键词: 双模耦合KdV方程, 简化的Hirota方法, 多孤子解, 周期解

Abstract: In this paper, multiple-soliton solutions for a new two-mode coupled KdV (nTMcKdV) equation are obtained by using the simplified Hirota's method and the Cole-Hopf transformation. It is shown that these types of multiple solutions exist only for models in which specific values for the nonlinearity and dispersion parameters are included in the models. Furthermore, other exact solutions for an nTMcKdV equation using general values of these parameters are derived by using several different expansion methods such as the tanh/coth method and the Jacobi elliptic function method.

Key words: two-mode coupled KdV equation, simplified Hirota's method, multiplesoliton solutions, periodic solutions

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