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arXiv · 1302.3814

Multi-solitary waves for the nonlinear Klein-Gordon equation

Jacopo Bellazzini·Marco Ghimenti·Stefan Le Coz
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Abstract

We consider the nonlinear Klein-Gordon equation in $\R^d$. 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.

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Jacopo Bellazzini, Marco Ghimenti, Stefan Le Coz. 2013-05-07. Multi-solitary waves for the nonlinear Klein-Gordon equation. https://doi.org/10.1080/03605302.2013.860988

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