Variational approximations for traveling solitons in a discrete nonlinear Schrödinger equation

Traveling solitary waves in the one-dimensional discrete nonlinear Schrödinger equation with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in analytical form. The stability is also studied by means of the VA, demonstrating that the soli...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-02, Vol.45 (7), p.75207-18
Main Authors: Syafwan, M, Susanto, H, Cox, S M, Malomed, B A
Format: Article
Language:English
Subjects:
Approximation
discrete Schrodinger equation
discrete soliton
Discretization
embedded soliton
Exact sciences and technology
Mathematical analysis
Mathematical models
Newton-Raphson method
Nonlinearity
Physics
saturable nonlinearity
Schroedinger equation
Solitary waves
Solitons
traveling soliton
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Summary:Traveling solitary waves in the one-dimensional discrete nonlinear Schrödinger equation with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in analytical form. The stability is also studied by means of the VA, demonstrating that the solitons are stable, which is consistent with previously published results. Then, the VA is applied to predict parameters of traveling solitons with non-oscillatory tails (embedded solitons, ESs). Two-soliton bound states are considered too. The separation distance between the solitons forming the bound state is derived by means of the VA. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton-Raphson method. In general, good agreement between the analytical and numerical results is obtained. In particular, we demonstrate the relevance of the analytical prediction of characteristics of the embedded solitons.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/7/075207