N-soliton states of the FPU lattices

Details N-soliton states of the FPU lattices N-soliton states of the FPU lattices

2010-04-15

arxiv.org/abs/1004.2646v1

Mathematics

Analysis of PDEs

33 pages, no figure.

Scientific paper

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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