一类广义浅水波KdV方程的可积性研究

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 451-460.

一类广义浅水波KdV方程的可积性研究

郝晓红¹(),程智龙^2,*()

¹ 苏州大学文正学院江苏苏州 215104
² 苏州科技大学数理学院江苏苏州 215009

收稿日期:2017-04-10 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 程智龙 E-mail:haoxiaohong200866@163.com;zhilong0793@sina.cn
作者简介:郝晓红, haoxiaohong200866@163.com
基金资助:
安徽省自然科学研究项目(KJ2016A071)

The Integrability of the KdV-Shallow Water Waves Equation

Xiaohong Hao¹(),Zhilong Cheng^2,*()

¹ Wenzheng College of Soochow University, Jiangsu Suzhou 215104
² School of Mathematics and Physics, Suzhou University of Sience and Technology, Jiangsu Suzhou 215009

Received:2017-04-10 Online:2019-06-26 Published:2019-06-27
Contact: Zhilong Cheng E-mail:haoxiaohong200866@163.com;zhilong0793@sina.cn
Supported by:
the Natural Science Foundation of Anhui Province(KJ2016A071)

摘要/Abstract

摘要：

该文应用双Bell多项式，系统研究了一类广义浅水波KdV方程的可积性.先构造出双线性表达式、Bäklund变换，再通过Bäklund变换线性化得到孤子解与Lax对.最后通过级数展开式代入得到无穷守恒律，从而证明此方程具有可积性.

关键词: Bäklund变换, Lax对, 无穷守恒律

Abstract:

In this paper, the binary Bell polynomials to construct bilinear forma, bilinear Bäcklund transformation, Lax pair of the KdV-shallow water waves equation. Through bilinear Bäcklund transformation, some soliton solutions are presented. Moreover, the infinite conservation laws are also derived by Bell polynomials, all conserved densities and fluxes are given with explicit recursion formulas.

Key words: Bäcklund transformation, Lax pair, Infinite conservation laws

中图分类号:

O175.24

郝晓红,程智龙. 一类广义浅水波KdV方程的可积性研究[J]. 数学物理学报, 2019, 39(3): 451-460.

Xiaohong Hao,Zhilong Cheng. The Integrability of the KdV-Shallow Water Waves Equation[J]. Acta mathematica scientia,Series A, 2019, 39(3): 451-460.

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