变系数5阶Korteweg-de Vries方程的Lax对和自-Bcklund变换研究  

The Lax pair and auto-Bcklund transformation for the variable-coefficient fifth-order Korteweg-de Vries equation

作　　者：王嘉谋[1] 王尚户[1] 何莉敏[1] 

机构地区：[1]内蒙古科技大学数理与生物工程学院,内蒙古包头014010

出　　处：《江苏科技大学学报（自然科学版）》2013年第3期303-306,共4页Journal of Jiangsu University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(81060238)

摘　　要：文中以在众多领域中存在广泛应用的变系数函数5阶Korteweg-de Vries方程为研究对象,首先基于Ablowitz-Kaup-Newell-Segur系统推出方程存在孤子解的约束条件和Lax对,进而构造方程的自-Bcklund变换和孤子解,并分析讨论变系数函数对孤子解传播特征的影响.A variable-coefficient fifth-order Korteweg-de Vries equation is investigated in this paper, which has a wide range of application in physics and engineering fields. Using the Ablowitz-Kaup-Newell-Segur system, the constraint for this model to have soliton solutions and Lax pair are derived. Moreover, the auto-Backlund trans- formation and solitonic solution are constructed. The influence of the variable-coefficient functions on propagation characteristics of the one solitonie solution is presented.

关 键 词：变系数5阶Korteweg—de VRIES方程 LAX对 自-Backlund变换 孤子解 

分 类 号：O175.29[理学—数学]