Multi-travelling waves for the nonlinear klein-gordon equation

TL;DR

This paper proves the existence of multi-solitary wave solutions for the nonlinear Klein-Gordon equation in one spatial dimension plus time, extending previous results limited to ground states to include multiple bound states.

Contribution

It generalizes prior work by establishing multi-solitary waves composed of any number of decoupled bound states, beyond just ground states.

Findings

Existence of multi-solitary wave solutions for the nonlinear Klein-Gordon equation.

Extension of previous results to include multiple bound states.

Broader class of solutions in nonlinear dispersive wave models.

Abstract

For the nonlinear Klein-Gordon equation in R 1+d , we prove the existence of multi-solitary waves made of any number N of decoupled bound states. This extends the work of C{\^o}te and Mu{\~n}oz (Forum Math. Sigma 2 (2014)) which was restricted to ground states, as were most previous similar results for other nonlinear dispersive and wave models.