Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation |
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Authors: | Jacopo Bellazzini Marco Ghimenti |
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Institution: | 1. Università degli Studi di Sassari , Sassari , Italy;2. Dipartimento di Matematica , Università di Pisa , Pisa , Italy |
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Abstract: | We consider the nonlinear Klein-Gordon equation in ? 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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Keywords: | Asymptotic behavior Klein-Gordon equation Multi-soliton |
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