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Solitary waves in the Ablowitz-Ladik equation with power-law nonlinearity
- Publication Year :
- 2018
-
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.
- Subjects :
- Nonlinear Sciences - Pattern Formation and Solitons
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1806.10898
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/1751-8121/aaf755