Quasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential

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dc.creatorJohansson, Magnus
dc.creatorGorbach, Andrey V.
dc.date2003-12-29
dc.date2004-08-30
dc.date.accessioned2026-07-07T05:35:15Z
dc.date.available2026-07-07T05:35:15Z
dc.descriptionWe present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schrödinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.
dc.description4 pages, 4 figures, to be published in Phys. Rev. E. Revised version: change of title, added Figs. 1(b),(c), 4 new references + minor clarifications
dc.identifierhttps://arxiv.org/abs/nlin/0312066
dc.identifierhttp://arxiv.org/abs/nlin/0312066
dc.identifierPhys. Rev. E 70, 057604 (2004)
dc.identifierdoi:10.1103/PhysRevE.70.057604
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80639
dc.subjectPattern Formation and Solitons
dc.subjectCondensed Matter
dc.subjectOptics
dc.titleQuasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential
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