数学季刊 ›› 2009, Vol. 24 ›› Issue (4): 525-536.

• • 上一篇    下一篇

(2+1)维KdV方程的新周期波之间的相互作用

  

  1. College of Science, Donghua University

  • 收稿日期:2007-06-06 出版日期:2009-12-30 发布日期:2023-06-16
  • 作者简介:GE Dong-jie(1982-), female, native of Shanghai, a master of Donghua University, engages in soliton and integrable system.
  • 基金资助:
    Supported by the National Natural Science Foundation of China(10647112,10871040);

New Periodic Wave Solutions and Their Interaction for (2+1)-dimensional KdV Equation

  1. College of Science, Donghua University
  • Received:2007-06-06 Online:2009-12-30 Published:2023-06-16
  • About author:GE Dong-jie(1982-), female, native of Shanghai, a master of Donghua University, engages in soliton and integrable system.
  • Supported by:
    Supported by the National Natural Science Foundation of China(10647112,10871040);

摘要: A class of new doubly periodic wave solutions for(2+1)-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution(contains two arbitrary functions) got by means of multilinear variable separation approach for(2+1)-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions,and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized.

关键词: (2+1)-dimensional KdV equation, multilinear variable separation approach, elliptic functions, periodic wave solutions, localized excitations, interaction property, nonelastic, completely elastic

Abstract: A class of new doubly periodic wave solutions for(2+1)-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution(contains two arbitrary functions) got by means of multilinear variable separation approach for(2+1)-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions,and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized.

Key words: (2+1)-dimensional KdV equation, multilinear variable separation approach, elliptic functions, periodic wave solutions, localized excitations, interaction property, nonelastic, completely elastic

中图分类号: