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Article Dans Une Revue Nonlinear Analysis Année : 2022

Kink networks for scalar fields in dimension 1+1

Résumé

We consider a scalar field equation in dimension $1+1$ with a positive external potential having non-degenerate isolated zeros. We construct weakly interacting pure multi-solitons, that is solutions converging exponentially in time to a superposition of Lorentz-transformed kinks, in the case of distinct velocities. We find that these solutions form a $2K$-dimensional smooth manifold in the space of solutions, where $K$ is the number of the kinks. We prove that this manifold is invariant under the transformations corresponding to the invariances of the equation, that is space-time translations and Lorentz boosts.
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hal-03365781 , version 1 (05-01-2024)

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Gong Chen, Jacek Jendrej. Kink networks for scalar fields in dimension 1+1. Nonlinear Analysis, 2022, 215, ⟨10.1016/j.na.2021.112643⟩. ⟨hal-03365781⟩
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