Kink networks for scalar fields in dimension 1+1

Gong Chen, Jacek Jendrej

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number112643
JournalNonlinear Analysis, Theory, Methods and Applications
StatePublished - Feb 2022

Bibliographical note

Funding Information:
J. Jendrej was supported by ANR-18-CE40-0028 project ESSED .

Publisher Copyright:
© 2021 Elsevier Ltd


  • Kink
  • Multi-soliton
  • Wave

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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