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Transactions of the American Mathematical Society

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Multi-travelling waves for the nonlinear Klein-Gordon equation


Authors: Raphaël Côte and Yvan Martel
Journal: Trans. Amer. Math. Soc. 370 (2018), 7461-7487
MSC (2010): Primary 35Q51; Secondary 35L71, 35Q40
DOI: https://doi.org/10.1090/tran/7303
Published electronically: June 20, 2018
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Abstract: For the nonlinear Klein-Gordon equation in $ \mathbb{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 Côte and Muñoz (Forum Math. Sigma 2 (2014)) which was restricted to ground states, as were most previous similar results for other nonlinear dispersive and wave models.


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Additional Information

Raphaël Côte
Affiliation: Université de Strasbourg, CNRS, IRMA UMR 7501, F-67000 Strasbourg, France
Email: cote@math.unistra.fr

Yvan Martel
Affiliation: CMLS, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
Email: yvan.martel@polytechnique.edu

DOI: https://doi.org/10.1090/tran/7303
Keywords: Klein-Gordon equation, multi-soliton, ground states, excited states, instability
Received by editor(s): December 6, 2016
Received by editor(s) in revised form: May 11, 2017
Published electronically: June 20, 2018
Additional Notes: The authors were supported in part by the ERC advanced grant 291214 BLOWDISOL. The first author was also supported in part by the ANR contract MAToS ANR-14-CE25-0009-01.
Article copyright: © Copyright 2018 American Mathematical Society

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