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Bcklund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.
出处
《中北大学学报（自然科学版）》
北大核心
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)
