摘要
修改 Korteweg-de Vries (mKdV ) 打了方程能被用来在液体，血浆，和光学描述某些非线性的现象。在这份报纸， discretized mKdV 格子方程被调查。在符号的计算的帮助下，分离矩阵光谱为那个系统的问题被构造。为那个系统的 Darboux 转变基于结果被建立光谱问题。明确的答案经由 Darboux 转变被导出。那些解决方案的结构图形地被显示出，它可能是有用的在液体，血浆，和光学理解一些物理进程。
The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.
基金
Supported by the National Natural Science Foundation of China under Grant No. 60772023
by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. BUAA-SKLSDE-09KF-04
Beijing University of Aeronautics and Astronautics, by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901
the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 200800130006
Chinese Ministry of Education, and Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No. KM201010772020
关键词
达布变换
德弗里斯
离散
方程
KDV
精确解
LATTICE
等离子体
Darboux transformation, discretized modified Korteweg-de Vries lattice equation, explicit solutions, symbolic computation
