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The closeness of localized structures between the Ablowitz-Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems
dc.creator | Hennig D., Karachalios N.I., Cuevas-Maraver J. | en |
dc.date.accessioned | 2023-01-31T08:28:07Z | |
dc.date.available | 2023-01-31T08:28:07Z | |
dc.date.issued | 2022 | |
dc.identifier | 10.1063/5.0072391 | |
dc.identifier.issn | 00222488 | |
dc.identifier.uri | http://hdl.handle.net/11615/73954 | |
dc.description.abstract | The Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localized solitons to rational solutions in the form of the spatiotemporally localized discrete Peregrine soliton. Proving a closeness result between the solutions of the Ablowitz-Ladik system and a wide class of Discrete Nonlinear Schrödinger systems in a sense of a continuous dependence on their initial data, we establish that such small amplitude waveforms may be supported in nonintegrable lattices for significantly large times. Nonintegrable systems exhibiting such behavior include a generalization of the Ablowitz-Ladik system with power-law nonlinearity and the discrete nonlinear Schrödinger equation with power-law and saturable nonlinearities. The outcome of numerical simulations illustrates, in excellent agreement with the analytical results, the persistence of small amplitude Ablowitz-Ladik analytical solutions in all the nonintegrable systems considered in this work, with the most striking example being that of the Peregine soliton. © 2022 Author(s). | en |
dc.language.iso | en | en |
dc.source | Journal of Mathematical Physics | en |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85129167036&doi=10.1063%2f5.0072391&partnerID=40&md5=05fddb392f201ca70efd27774265a75e | |
dc.subject | American Institute of Physics Inc. | en |
dc.title | The closeness of localized structures between the Ablowitz-Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems | en |
dc.type | journalArticle | en |
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