(2+1)维KdV方程的Bcklund变换和无穷守恒律  

The Bcklund Transformation and Infinite Conservation Laws of(2+1)Dimensional KdV Equation

作　　者：郭婷婷[1] 

机构地区：[1]山西大学商务学院,山西太原030031

出　　处：《中北大学学报（自然科学版）》2017年第3期277-281,共5页Journal of North University of China(Natural Science Edition)

基　　金：山西大学商务学院科研基金资助项目(2016028)

摘　　要：对双Bell多项式进行研究,并基于多维双Bell多项式和标准的Hirota双线性方程之间的关系,构造出(2+1)维KdV方程带有任意函数的双线性表达式.运用双Bell恒等式,确定(2+1)维KdV方程的双线性Bcklund变换.通过做变量变换,将(2+1)维KdV方程的耦合系统线性化为含有多个参数的Lax对,并证明其满足可积性条件.此外,求得这个非线性发展方程的无穷守恒律,并准确地给出所有守恒密度和流量的递推公式.The binary Bell polynomials are researched, based on the link between multi-dimensional binary Bell polynomials and the standard Hirota bilinear equation, the bilinear expressions with arbitrary function for （2＋1） dimensional KdV equation are constructed, the approach is different from the Hirota bilinear method.By application of binary Bell identity, the bilinear B（a）cklund transformations of the （2＋1） dimensional KdV equation are obtained.By means of variate transformation, the coupled system of the （2＋1） dimensional KdV equation is linearized into Lax pairs with multi-parameters, it is proved that the integrability condition is satisfied.In addition, the infinite conservation laws of this nonlinear evolution equation are derived, all conserved densities and fluxes are given with explicit recursion formulas.

关 键 词：双Bell多项式 (2+1)维KdV方程 Bcklund变换 无穷守恒律 LAX对 

分 类 号：O129.35[理学—数学]