Article
Solitary waves in the Ablowitz--Ladik equation with power-law nonlinearity
Author/s | Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G. Malomed, Boris A. Guo, Lijuan |
Department | Universidad de Sevilla. Departamento de Física Aplicada I |
Publication Date | 2019 |
Deposit Date | 2019-05-15 |
Published in |
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Abstract | We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr¨odinger equation with the same type of the nonlinearity. The model
opens a ... We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr¨odinger equation with the same type of the nonlinearity. The model opens a way to study the interplay of discreteness and nonlinearity features. We identify stationary discretesoliton states for different values of nonlinearity power σ, and address changes of their stability as frequency ω of the standing wave varies for given σ. Along with numerical methods, a variational approximation is used to predict the form of the discrete solitons, their stability changes, and bistability features by means of the Vakhitov-Kolokolov criterion (developed from the first principles). Development of instabilities and the resulting asymptotic dynamics are explored by means of direct simulations. |
Project ID. | MAT2016-79866-R |
Citation | Cuevas-Maraver, J., Kevrekidis, P.G., Malomed, B.A. y Guo, L. (2019). Solitary waves in the Ablowitz--Ladik equation with power-law nonlinearity. Journal of Physics A: Mathematical and Theoretical, 52 (6), 065202-. |
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