Kink networks for scalar fields in dimension 1+1. (February 2022)

• Record Type: Journal Article
• Authors: Chen, Gong; Jendrej, Jacek
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: Wave -- Kink -- Multi-soliton; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112643
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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 2 K -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.