N-soliton states of the FPU lattices

TL;DR

This paper proves the existence and uniqueness of multi-soliton solutions in the FPU lattice, demonstrating that solutions can asymptotically resemble a sum of co-propagating solitary waves, extending understanding of soliton interactions.

Contribution

It establishes the existence and uniqueness of multi-soliton solutions in the FPU lattice using linear stability analysis in weighted spaces, a novel approach in this context.

Findings

Solutions converge to a sum of co-propagating solitons as time approaches infinity.

The paper extends stability analysis techniques to multi-soliton solutions in discrete lattices.

It provides a rigorous mathematical foundation for multi-soliton states in the FPU model.

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].