Kink dynamics in spatially inhomogeneous media: the role of internal modes

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Show simple item record González, Jorge A. Cuenda, Sara Sánchez, Angel 2012-09-04T08:14:52Z 2012-09-04T08:14:52Z 2007-03
dc.identifier.bibliographicCitation Physical Review E, vol. 75, n. 3, mar. 2007. Pp. 1-7
dc.identifier.issn 1539-3755 (print version)
dc.identifier.issn 1550-2376 (online version)
dc.description.abstract The phenomenon of length-scale competition in soliton-bearing equations perturbed by spatially dependent terms A. Sánchez and A. R. Bishop, SIAM Rev. 40, 579 1998 is analyzed from a general viewpoint. We show that the perturbation gives rise to an effective potential for solitons, which consists of wells and barriers. We calculate the effect of these potential features on the solitons, establishing a direct relationship between the maxima, minima, and curvature of the potential with soliton deformations. When the typical wavelength of the perturbation is of the order of the soliton width, these deformations are seen to correspond to the excitation of shape modes and can lead to the dissipation of the soliton kinetic energy and, further, to the impossibility of soliton propagation. Thus, we demonstrate that the mechanism for length-scale competition is related to changes in the dynamics of the internal modes. We study different examples where the perturbation is introduced parametrically and nonparametrically to make it clear that our results apply to a wide class of equations.
dc.description.sponsorship This work was supported by MEC Spain under Grants MOSAICO and No. NAN2004-9087-C03-03 and by the Comunidad Autónoma de Madrid (Spain) under Grants No. UC3M-FI-05-007 and SIMUMAT-CM. The work by J.G. was done in part during a stay at Universidad Carlos III de Madrid, whose financial support is acknowledged, and S.C. is supported by the Consejería de Educación de la Comunidad Autónoma de Madrid and the Fondo Social Europeo.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher American Physical Society
dc.title Kink dynamics in spatially inhomogeneous media: the role of internal modes
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1103/PhysRevE.75.036611
dc.rights.accessRights openAccess
dc.type.version publishedVersion
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