FPU晶格的N孤子态
N-soliton states of the FPU lattices
摘要：
本文利用[Mizumachi，arXiv：0906.1320]证明的指数加权空间中多类孤子解的线性稳定性，证明了Fermi Pasta Ulam格点方程解的存在唯一性，使其收敛于一个共同传播的$N$孤波之和$t\to\infty$.反向传播的两个孤子态已经由[Hoffman和Wayne，Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model，J. Dynam.微分方程21（2009），343-351]。
英文摘要：
In this paper, we prove existence and uniqueness of solutions to the Fermi Pasta Ulam lattice equation that converge to a sum of co-propagating $N$ solitary waves as $t\to\infty$ using linear stability property of multi-soliton like solutions in an exponentially weighted space proved by [Mizumachi, arXiv:0906.1320]. Counter-propagating two soliton states have been studied by [Hoffman and Wayne, Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model, J. Dynam. Differential Equations 21 (2009), 343-351].
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