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arXiv · 1607.06421

Nonexistence of small, odd breathers for a class of nonlinear wave equations

Michał Kowalczyk·Yvan Martel·Claudio Muñoz
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Abstract

In this note, we show that for a large class of nonlinear wave equations with odd nonlinearities, any globally defined odd solution which is small in the energy space decays to $0$ in the local energy norm. In particular, this result shows nonexistence of small, odd breathers for some classical nonlinear Klein Gordon equations such as the sine Gordon equation and $ϕ^4$ and $ϕ^6$ models. It also partially answers a question of Soffer and Weinstein in \cite[p. 19]{MR1681113} about nonexistence of breathers for the cubic NLKG in dimension one.

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Michał Kowalczyk, Yvan Martel, Claudio Muñoz. 2016-07-21. Nonexistence of small, odd breathers for a class of nonlinear wave equations. https://doi.org/10.1007/s11005-016-0930-y

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