Artículo
The closeness of localized structures between the Ablowitz-Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems
Autor/es | Hennig, Dirk
Karachalios, Nikos I. Cuevas-Maraver, Jesús |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada I |
Fecha de publicación | 2022-05 |
Fecha de depósito | 2023-01-16 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | EU (FEDER program 2014-2020) and Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía P18-RT-3480 EU (FEDER program 2014-2020) and Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía US-1380977 MICINN and AEI PID2019-110430GB-C21 MICINN and AEI PID2020-112620GB-I00 |
Identificador del proyecto | P18-RT-3480
US-1380977 PID2019-110430GB-C21 PID2020-112620GB-I00 |
Cita | Hennig, D., Karachalios, N.I. y Cuevas-Maraver, J. (2022). The closeness of localized structures between the Ablowitz-Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems. Journal of Mathematical Physics, 63 (4). https://doi.org/10.1063/5.0072391. |
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