摘要
利用外微分形式系统和Lie代数表示理论提出了求解非线性波方程Lax对的延拓结构理论,该方法是构造非线性波方程Lax对的系统最有效的方法.其关键在于如何给出延拓代数的具体表示,如微分算子表示或矩阵表示.如果一个非线性波方程具有非平凡的延拓代数,则称其延拓代数可积,本篇论文主要利用延拓结构理论,讨论KdV方程的解,同时给出了带一个参数的特殊KdV方程的线性谱问题.
This paper the differential system and Lie algebra expression theory to point out the continuation structure theory for solving the nonlinear wave equation. This method is a systematic and effective way tostructure the nonlinear wave equation Lax pair. The key is on how to point out the detailed expressions of continuation algebra, such as differential operator and matrix expression. If a nonlinear wave equation has an uncommon continuation algebra, it can be said that its continuation structure is integrable. This is the key research method of this paper. The theory of prolongation structure is used to discuss the special KdV Equation.We also present the linear spectral problem of the special KdV equation with a parameter.
出处
《纯粹数学与应用数学》
CSCD
2011年第1期27-31,共5页
Pure and Applied Mathematics
基金
国家教育部高等学校特色专业建设点-数学与应用数学(藏汉双语)项目(TS2413)
关键词
李代数
延拓结构
LAX对
线性谱问题
Lie algebra
prolongation structure
Lax pair
linear spectral problem
