贝尔多项式方法在6阶KdV方程的应用  

Application of Bell-polynomial method in the sixth-order KdV equation

作　　者：余兰 张玉平[1] 魏光美[2] YU Lan;ZHANG Yuping;WEI Guangmei(School of Computer Science and Engineering, Beihang University, Beijing 100083, China;School of Mathematics and System Sciences, Beihang University, Beijing 100083, China)

机构地区：[1]北京航空航天大学计算机学院,北京100083 [2]北京航空航天大学数学与系统科学学院,北京100083

出　　处：《北京信息科技大学学报（自然科学版）》2018年第2期16-19,共4页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金项目(61471406;11401031)

摘　　要：对高阶非线性方程的可积性研究仍是一大难点。通过贝尔多项式方法对6阶Kd V方程进行可积性研究和求解。首先通过构造贝尔多项式的几种组合,推导出带有辅助自变量的双线性形式,进而求得该方程的N孤子解。基于贝尔多项式形式的双线性形式,通过符号计算,得到方程的Bcklund变换,Lax对和无穷守恒律。The integrability and solution of sixth-order Korteweg-de Vries（ Kd V） equation is studied by Bell-polynomial method. By constructing several combinations of Bell polynomials, the bilinear form with an auxiliary argument is deduced,and the N-soliton solution of this equation is obtained. Based on the bilinear form of the Bell-polynomial form,Bcklund transformation,Lax pair and infinite numbers of conservation laws of the equation are derived by symbolic computation.

关 键 词：6阶KdV方程 贝尔多项式方法 孤子解 BACKLUND变换 符号计算 守恒律 

分 类 号：O29[理学—应用数学]