一类广义浅水波KdV方程的可积性研究  

The Integrability of the KdV-Shallow Water Waves Equation

作　　者：郝晓红 程智龙 Xiaohong Hao;Zhilong Cheng(Wenzheng College of Soochow University, Jiangsu Suzhou 215104;School of Mathematics and Physics, Suzhou University of Sience and Technology, Jiangsu Suzhou 215009)

机构地区：[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

出　　处：《数学物理学报（A辑）》2019年第3期451-460,共10页Acta Mathematica Scientia

基　　金：安徽省自然科学研究项目(KJ2016A071)~~

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、Baklund变换,再通过Baklund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.In this paper, the binary Bell polynomials to construct bilinear forma, bilinear Backlund transformation, Lax pair of the KdV-shallow water waves equation. Through bilinear Backlund 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.

关 键 词：Baklund变换 LAX对 无穷守恒律 

分 类 号：O175.24[理学—数学]