Normal form for travelling kinks in discrete Klein–Gordon lattices
| Autor: | Dmitry E. Pelinovsky, Gérard Iooss |
|---|---|
| Přispěvatelé: | Institut Non Linéaire de Nice Sophia-Antipolis (INLN), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Statistics [Hamilton], McMaster University [Hamilton, Ontario] |
| Jazyk: | angličtina |
| Rok vydání: | 2006 |
| Předmět: |
Discretization
Differential equation Dynamical Systems (math.DS) sine-Gordon equation Normal forms 01 natural sciences Heteroclinic orbits 010305 fluids & plasmas Klein–Gordon lattices symbols.namesake 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics Travelling kinks Existence and persistence analysis Mathematics - Dynamical Systems 0101 mathematics Klein–Gordon equation Nonlinear Sciences::Pattern Formation and Solitons Eigenvalues and eigenvectors Mathematics Mathematical physics Equilibrium point 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Condensed Matter Physics 37K60 Nonlinear system Mathematics - Classical Analysis and ODEs Discrete equations symbols Heteroclinic orbit Centre manifold |
| Zdroj: | Physica D: Nonlinear Phenomena Physica D: Nonlinear Phenomena, Elsevier, 2006, 216, pp.327-345. ⟨10.1016/j.physd.2006.03.012⟩ |
| ISSN: | 0167-2789 |
| DOI: | 10.1016/j.physd.2006.03.012⟩ |
| Popis: | We study travelling kinks in the spatial discretizations of the nonlinear Klein–Gordon equation, which include the discrete ϕ 4 lattice and the discrete sine-Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically the non-existence of monotonic kinks (heteroclinic orbits between adjacent equilibrium points) in the fourth-order equation. Making generic assumptions on the reduced fourth-order equation, we prove the persistence of bounded solutions (heteroclinic connections between periodic solutions near adjacent equilibrium points) in the full differential advance-delay equation with the technique of centre manifold reduction. Existence of multiple kinks in the discrete sine-Gordon equation is discussed in connection to recent numerical results of Aigner et al. [A.A. Aigner, A.R. Champneys, V.M. Rothos, A new barrier to the existence of moving kinks in Frenkel–Kontorova lattices, Physica D 186 (2003) 148–170] and results of our normal form analysis. |
| Databáze: | OpenAIRE |
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