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Pré-Publication, Document De Travail Année : 2023

Asymptotic stability and classification of multi-solitons for Klein-Gordon equations

Résumé

Focusing on multi-solitons for the Klein-Gordon equations, in first part of this paper, we establish their conditional asymptotic stability. In the second part of this paper, we classify pure multi-solitons which are solutions converging to multi-solitons in the energy space for large time. Using Strichartz estimates developed in our earlier work and the modulation techniques, we show that if a solution stays close to the multi-soliton family, then it scatters to the multi-soliton family in the sense that the solution will converge in large time to a superposition of Lorentz-transformed solitons (with slightly modified velocities), and a radiation term which is at main order a free wave. Moreover, we construct a finite-codimension centre-stable manifold around the well-separated multi-soliton family. Finally, given different Lorentz parameters and arbitrary centers, we show that all the corresponding pure multi-solitons form a finite-dimension manifold.

Dates et versions

hal-03964308 , version 1 (31-01-2023)

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Gong Chen, Jacek Jendrej. Asymptotic stability and classification of multi-solitons for Klein-Gordon equations. 2023. ⟨hal-03964308⟩
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