Comparative Study of Different Discretizations of the $ϕ^4$ Model

Simple item page
dc.creatorRoy, Ishani
dc.creatorDmitriev, Sergey V.
dc.creatorKevrekidis, Panayotis G.
dc.creatorSaxena, Avadh
dc.date2006-08-19
dc.date.accessioned2026-07-07T11:07:22Z
dc.date.available2026-07-07T11:07:22Z
dc.descriptionWe examine various recently proposed discretizations of the well-known $ϕ^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral properties of the linearization around such waves. We study these features as a function of the lattice spacing $h$, as one deviates from the continuum limit of $h \to 0$. We then proceed to a more ``stringent'' comparison of the models, by discussing the scattering properties of a kink-antikink pair for the different discretizations. These collisions are well-known to possess properties that quite sensitively depend on the initial speed even at the continuum limit. We examine how typical model behaviors are modified in the presence (and as a function) of discreteness and attempt to extract qualitative trends and issue pertinent warnings about some of the surprising resulting properties.
dc.description21 pages, 16 figures. Submitted for publication
dc.identifierhttps://arxiv.org/abs/nlin/0608046
dc.identifierhttp://arxiv.org/abs/nlin/0608046
dc.identifierPhys.Rev.E76:026601,2007
dc.identifierdoi:10.1103/PhysRevE.76.026601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189819
dc.subjectPattern Formation and Solitons
dc.subjectExactly Solvable and Integrable Systems
dc.titleComparative Study of Different Discretizations of the $ϕ^4$ Model
dc.typetext

Files

Collections

arXiv