7阶Lax方程的Lax对、守恒律、达布变换及解析解  

Lax pair,conservation laws,Darboux transformation and analytic solution for seventh-order Lax equation

作　　者：郑文鑫[1] 魏光美[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《北京信息科技大学学报（自然科学版）》2017年第1期20-23,共4页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金资助项目(61471406)

摘　　要：7阶Lax方程是重要的可积高阶Kd V方程。利用伪势方法,求得方程组形式的Lax对和AKNS形式的Lax对。根据方程组形式的Lax对,推导方程的无穷守恒律。由AKNS形式的Lax对构造达布变换,最后由达布变换推出方程的孤子解。Seventh-order Lax equation as the higher order Kd V equation has been testified to satisfy Painlevé integrability. Two sets of Lax pair of seventh-order equation can be derived from the poseudopotentials approach. Based on Lax pair in form of equations,infinite numbers of conservation laws are obtained,while Darboux transformation is constructed by the Lax pair in form of AKNS system.Finally,one-soliton solution is presented by the Darboux transformation.

关 键 词：7阶Lax方程 LAX对 守恒律 达布变换 解析解 

分 类 号：O29[理学—应用数学]