Doubly periodic waves of a discrete nonlinear Schr\"odinger system with saturable nonlinearity
Robert Conte, Kwok-wing Chow
TL;DR
This paper investigates doubly periodic wave solutions in a discrete nonlinear Schrödinger system with saturable nonlinearity, deriving their long wave limits and providing new elliptic solutions for related systems.
Contribution
It introduces novel doubly periodic wave solutions for a discrete nonlinear Schrödinger system with saturable nonlinearity and derives their long wave limits.
Findings
Existence of doubly periodic wave solutions in the system
Derivation of long wave limits of these solutions
Provision of new elliptic solutions for NLS-type systems
Abstract
A system of two discrete nonlinear Schr\"odinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-product, several new solutions of the elliptic type are provided for NLS-type discrete and continuous systems.
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