N-soliton states of the FPU lattices

Abstract

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].