Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction

DOI10.1016/J.NA.2008.04.018zbMath1160.37415OpenAlexW2064470428WikidataQ59902261 ScholiaQ59902261MaRDI QIDQ1009630

Carl-Friedrich Kreiner, Johannes Zimmer

Publication date: 2 April 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://opus.bath.ac.uk/14003/1/Zimmer_NATMA_2009_90_9_3146.pdf

zbMATH Keywords

travelling wavescalculus of variationsconcentration compactnessnonlinear Klein-Gordon lattice

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Nonlinear waves in solid mechanics (74J30) Existence of solutions for minimax problems (49J35) Lattice dynamics; integrable lattice equations (37K60)

Related Items (10)

Traveling kinks in an infinite array of weakly coupled pendula ⋮ Periodic traveling waves in the system of linearly coupled nonlinear oscillators on 2D-lattice ⋮ Existence of homoclinic orbits of a class of second-order quasilinear Schrödinger equations with delay ⋮ Periodic traveling wave solutions of discrete nonlinear Klein‐Gordon lattices ⋮ Periodic and homoclinic travelling waves in infinite lattices ⋮ Action minimising fronts in general FPU-type chains ⋮ Uniform sliding states in the undamped Frenkel-Kontorova model ⋮ Periodic travelling waves in convex Klein-Gordon chains ⋮ Unnamed Item ⋮ Homoclinic traveling waves in discrete sine-Gordon equation with nonlinear interaction on 2D-lattice

Cites Work

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• On the lowest eigenvalue of the Laplacian for the intersection of two domains
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction
• Solitary waves for nonconvex FPU lattices
• Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction
• Existence theorem for solitary waves on lattices
• Multibump periodic motions of an infinite lattice of particles
• Solitary waves with prescribed speed on infinite lattices
• Minimax theorems

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