Kink networks for scalar fields in dimension 1+1

Gong Chen (1) , Jacek Jendrej (2)

1 Department of Mathematics [University of Toronto]
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Equations aux dérivées partielles [math.AP]

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⟩