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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 33-39.doi: 10.6040/j.issn.1671-9352.0.2024.175

• • 上一篇    

新的(2+1)维Boussinesq方程的孤立子解

郭学军,曹玉雷*   

  1. 南阳理工学院数理学院, 河南 南阳 473004
  • 发布日期:2025-05-19
  • 通讯作者: 曹玉雷(1993— ),男,讲师,博士,研究方向为孤立子与可积系统. E-mail:caoyulei@mail.ustc.edu.cn
  • 作者简介:郭学军(1966— ),男,教授,研究方向为孤立子与可积系统. E-mail:gxuejun66@163.com*通信作者:曹玉雷(1993— ),男,讲师,博士,研究方向为孤立子与可积系统. E-mail:caoyulei@mail.ustc.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12301312)

Soliton solutions of the new(2+1)-dimensional Boussinesq equation

GUO Xuejun, CAO Yulei*   

  1. School of Mathematics and Physics, Nanyang Institute of Technology, Nanyang 473004, Henan, China
  • Published:2025-05-19

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摘要： 研究(2+1)维的Boussinesq方程,该系统是Boussinesq方程的一个多维推广版本。利用Hirota的双线性方法构造(2+1)维Boussinesq方程的孤立子解,并分析孤立子解的局部特征,给出了孤立子解的动力学行为。此外,在特殊参数限制下得到了共振的孤立子解。由于共振碰撞,孤立子解呈现“V”型,不再是传统的交叉型。更高阶的共振孤立子解的动力学行为更加复杂多样,由基本的共振孤立子叠加而成。

关键词: (2+1)-维Boussinesq方程, 双线性方法, 孤立子解, 动力学

Abstract: The(2+1)-dimensional Boussinesq equation is investigated, which is a multidimensional extension of the typical Boussinesq equation. The soliton solutions of(2+1)-dimensional Boussinesq equation are constructed by using the Hirota bilinear method. The local characteristics of the soliton solutions are also analyzed, and the dynamic behaviors of these soliton solutions are given analytically. Additionally, under the limitation of special parameters, we also obtain the resonance soliton solutions, and due to the resonance collision, the soliton solution presents a "V" shape, which is no longer the traditional cross type. The dynamics of higher-order resonance soliton solutions are more complex and diverse, consisting of the superposition of fundamental resonant solitons.

Key words: (2+1)-dimensional Boussinesq equation, bilinear method, soliton solution, dynamics

中图分类号: 

  • O175.29
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