Exact Localized Solutions of Quintic Discrete Nonlinear Schrödinger Equation

Abstract

We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form ${\varphi }_{n+1}+{\varphi }_{n-1}=F({\varphi }_n)$. Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.

12 pages,4 figures(eps files),revised,Physics Letters A, In press

References in corpus (3)

• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Spatial optical solitons in nonlinear photonic crystals
• Exact soliton solutions of the one-dimensional complex Swift-Hohenberg equation

Cited by in corpus (4)

• Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model
• Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities
• Forced Nonlinear Schroedinger Equation with Arbitrary Nonlinearity
• The exact solutions and their linear stability analysis for 2-dimensional Ablowitz-Ladik equation