Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model

TL;DR

This paper proves the existence of solutions in the Fermi-Pasta-Ulam model that asymptotically resemble two solitary waves, demonstrating their long-term stability and interaction behavior.

Contribution

It establishes the existence of asymptotic two-soliton states in the Fermi-Pasta-Ulam model with general interaction potentials, a novel theoretical result.

Findings

Existence of asymptotic two-soliton solutions

Solutions converge to superpositions of two solitary waves

Applicable to general interaction potentials

Abstract

We prove the existence of asymptotic two-soliton states in the Fermi-Pasta-Ulam model with general interaction potential. That is, we exhibit solutions whose difference in $\ell^2$ from the linear superposition of two solitary waves goes to zero as time goes to infinity.