数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1064-1076.

• 论文 • 上一篇    

(3+1)维广义Kadomtsev-Petviashvili方程新的精确周期孤立波解

李颖1, 刘建国2, 阳连武1   

  1. 1 宜春学院数学与计算机科学学院 江西宜春 336000;
    2 江西中医药大学计算机学院 南昌 330004
  • 收稿日期:2018-08-30 修回日期:2018-11-23 发布日期:2019-11-08
  • 通讯作者: 李颖 E-mail:jxsdsxx@bupt.edu.cn
  • 基金资助:
    国家自然科学基金(61377067)和江西省教育厅科技项目(GJJ170889)

New Exact Periodic Solitary Wave Solutions for the (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation

Li Ying1, Liu Jianguo2, Yang Lianwu1   

  1. 1 School of Mathematical and Computer Science, Yichun University, Jiangxi Yichun 336000;
    2 College of Computer, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004
  • Received:2018-08-30 Revised:2018-11-23 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (61377067) and the Jiangxi Provincial Department of Education (GJJ170889)

摘要: 该文研究了广义Kadomtsev-Petviashvili方程,该方程是依赖于横坐标的小振幅慢波非线性长波演化方程.利用Hirota的双线性形式与扩展同宿测试方法,(3+1)维广义Kadomtsev-Petviashvili方程新的精确周期孤立波解被获得,这些获得的结果和已知文献中的结论都不同.在符号计算的帮助下,这些新的周期波精确解的性质和特点通过一些图形进行了展示.

关键词: Hirota双线性形式, 周期孤立波解, 扩展同宿测试方法, 广义Kadomtsev-Petviashvili方程

Abstract: In this paper, we investigate the generalized Kadomtsev-Petviashvili equation for the evolution of nonlinear, long waves of small amplitude with slow dependence on the transverse coordinate. By virtue of the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary wave solutions for the (3+1)-dimensional generalized KadomtsevPetviashvili equation are obtained, which is different from those in previous literatures. With the aid of symbolic computation, the properties and characteristics for these new exact periodic wave solutions are presented with some figures.

Key words: Hirota's bilinear form, Periodic solitary wave solutions, Extended homoclinic test approach, Generalized Kadomtsev-Petviashvili equation

中图分类号: 

  • O175.2