Multi-solitary waves for the nonlinear Klein-Gordon equation
Analysis of PDEs
2014-10-01 v2 Mathematical Physics
math.MP
Abstract
We consider the nonlinear Klein-Gordon equation in . We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates.
Cite
@article{arxiv.1302.3814,
title = {Multi-solitary waves for the nonlinear Klein-Gordon equation},
author = {Jacopo Bellazzini and Marco Ghimenti and Stefan Le Coz},
journal= {arXiv preprint arXiv:1302.3814},
year = {2014}
}