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arXiv · 1806.10898

Solitary waves in the Ablowitz-Ladik equation with power-law nonlinearity

J. Cuevas-Maraver·P. G. Kevrekidis·B. A. Malomed·L. Guo
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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\"{o}dinger 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 discrete-soliton states for different values of nonlinearity power $\sigma $, and address changes of their stability as frequency $\omega $ of the standing wave varies for given $\sigma $. 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.

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J. Cuevas-Maraver, P. G. Kevrekidis, B. A. Malomed, L. Guo. 2018-06-28. Solitary waves in the Ablowitz-Ladik equation with power-law nonlinearity. https://doi.org/10.1088/1751-8121/aaf755

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