Asymptotic stability of Toda lattice solitons
Asymptotic stability of Toda lattice solitons
复制标题
DOI：
10.1088/0951-7715/21/9/011
复制
发表时间：
2008-09
期刊：
影响因子：
1.7
通讯作者：
Tetsu Mizumachi;R. Pego
中科院分区：
文献类型：
--
作者：
Tetsu Mizumachi;R. Pego
利用线性化的Bäcklund变换，得到了户田格点孤子解的一个渐近稳定性结果.将线性稳定性结果与Friesecke和Pego关于格点方程中孤立波的非线性稳定性的一般理论相结合，我们得出结论：户田格点中的所有孤立波在指数加权范数下是渐近稳定的.此外，我们确定了完整的频谱运营商自然与Floquet理论为这些晶格孤子。
We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of a linearized Bäcklund transformation whose domain has codimension one. Combining a linear stability result with a general theory of nonlinear stability by Friesecke and Pego for solitary waves in lattice equations, we conclude that all solitons in the Toda lattice are asymptotically stable in an exponentially weighted norm. In addition, we determine the complete spectrum of an operator naturally associated with the Floquet theory for these lattice solitons.