The global structure of traveling waves in spatially discrete dynamical systems

被引：214
作者：
Mallet-Paret J. [1 ]
机构：
[1] Division of Applied Mathematics, Brown University, Providence
来源：
Journal of Dynamics and Differential Equations | 1999年 / 11卷 / 1期
基金：
美国国家科学基金会;
关键词：
Continuation methods; Heteroclinic orbits; Lattice differential equations; Lin's method; Mel'nikov method; Spatially discrete systems; Traveling waves;
D O I：
10.1023/A:1021841618074
中图分类号：
学科分类号：
摘要：
We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely, lattice differential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c ≠ 0, are also shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where c ≠ 0. Convergence results for solutions are obtained at the singular perturbation limit c → 0. © 1999 Plenum Publishing Corporation.
引用
收藏
页码：49 / 127
页数：78
相关论文
共 50 条
12345