Asymptotics for kink propagation in the discrete Sine-Gordon equation

The evolution of a propagating kink in a Sine-Gordon lattice is studied asymptotically using an averaged Lagrangian formulation appropriately coupled to the effect of the radiation. We find that unlike the continuum case the interaction with the Goldstone mode is important to explain the acceleratio...

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Detalles Bibliográficos
Autores: Cisneros, LA, Minzoni, AA
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:México
Institución:Universidad Nacional Autónoma de México
Repositorio:Sistema de Información de la Facultad de Ciencias, UNAM
OAI Identifier:oai:repositorio.fciencias.unam.mx:11154/1010
Acceso en línea:http://hdl.handle.net/11154/1010
Access Level:acceso abierto
Palabra clave:Mathematics, Applied
Physics, Multidisciplinary
Physics, Mathematical
kink
Peierls-Nabarro potential
radiation damping
internal modes
modulation averaged Lagrangian
Descripción
Sumario:The evolution of a propagating kink in a Sine-Gordon lattice is studied asymptotically using an averaged Lagrangian formulation appropriately coupled to the effect of the radiation. We find that unlike the continuum case the interaction with the Goldstone mode is important to explain the acceleration of the kink as it hops along the lattice. We develop a discrete WKB type solution to study the interaction of the kink and the radiation. In particular using this solution we show how to calculate the effect of the Peyrard and Kruskal resonant radiation in the energy loss of the kink. We obtain a set of modulation equation which explains qualitatively the evolution of the kink with remarkable quantitative agreement. (c) 2007 Elsevier B.V. All rights reserved.