Kink networks for scalar fields in dimension 1+1
| Autor: | Jacek Jendrej, Gong Chen |
|---|---|
| Přispěvatelé: | Department of Mathematics [University of Toronto], University of Toronto, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
Lorentz transformation 010102 general mathematics Scalar (mathematics) Space (mathematics) 01 natural sciences Manifold 010305 fluids & plasmas Superposition principle symbols.namesake Mathematics - Analysis of PDEs Dimension (vector space) 0103 physical sciences FOS: Mathematics symbols [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Invariant (mathematics) Scalar field Analysis Analysis of PDEs (math.AP) Mathematics Mathematical physics |
| Zdroj: | Nonlinear Analysis Nonlinear Analysis, In press Nonlinear Analysis, In press, 215, ⟨10.1016/j.na.2021.112643⟩ |
| DOI: | 10.1016/j.na.2021.112643⟩ |
| Popis: | 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. Comment: 22 pages |
| Databáze: | OpenAIRE |
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