一个离散MKdV方程的可积性检验  

The Integrability Test of a Discrete Model of the MKdV Equation

作　　者：白永强[1,2] 李挡振[2] 裴明[2] 

机构地区：[1]河南大学现代数学研究所,河南开封475004 [2]河南大学数学与统计学院,河南开封475004

出　　处：《河南大学学报（自然科学版）》2015年第2期131-133,共3页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(10801045)

摘　　要：延拓结构理论是求非线性演化方程拉克斯对、贝克隆变换、守恒量等的一种重要方法,由该方程的拉克斯对可以检验其可积性.基于非交换外微分,这一理论最近被推广到微分差分方程中去了.在本文中,利用半离散的延拓结构理论讨论了形变KdV(MKdV)方程的一个离散模型,得到了其延拓结构和拉克斯对,由此检验了这一方程的可积性.The theory of prolongation structure is an important methodology to get the Lax pair,Backlund transformation and conservation law of nonlinear evolution equations.The integrability of the nonlinear equation can be tested from its Lax pair.Based on the theory of noncommutative exterior differential calculus,the theory of prolongation structure has been generalized to differential-difference case.In this paper,we discuss the semi-discrete MKdV equation in terms of the semidiscrete prolongation structure theory and obtain its Lax pair.Therefore,the integrability of the differential-difference can be tested.

关 键 词：非交换微分 延拓结构 拉克斯对 

分 类 号：O175.7[理学—数学]