Artículo
The closeness of the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation
Autor/es | Hennig, Dirk
Karachalios, Nikos I. Cuevas-Maraver, Jesús |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada I |
Fecha de publicación | 2022-04 |
Fecha de depósito | 2022-03-22 |
Publicado en |
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Resumen | While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of ... While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of a “continuous dependence” on their initial data in the and metrics. The most striking relevance of the analytical results is that small amplitude solutions of the Ablowitz-Ladik system persist in the Discrete Nonlinear Schrödinger one. It is shown that the closeness results are also valid in higher dimensional lattices, as well as, for generalised nonlinearities. For illustration of the applicability of the approach, a brief numerical study is included, showing that when the 1-soliton solution of the Ablowitz-Ladik system is initiated in the Discrete Nonlinear Schrödinger system with cubic or saturable nonlinearity, it persists for long-times. Thereby, excellent agreement of the numerical findings with the theoretical predictions is obtained. |
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 the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation. Journal of Differential Equations, 316, 346-363. |
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