Gap Solitons in Periodic Discrete Nonlinear Schroedinger Equations

Abstract

It is shown that the periodic DNLS, with cubic nonlinearity, possesses gap solutions, i. e. standing waves, with the frequency in a spectral gap, that are exponentially localized in spatial variable. The proof is based on the linking theorem in combination with periodic approximations.

References in corpus (5)

• Discrete Breathers
• Excitation Thresholds for Nonlinear Localized Modes on Lattices
• On classification of intrinsic localized modes for the Discrete Nonlinear Schrödinger Equation
• Generation and stability of discrete gap solitons
• Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model

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• Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization
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• On-Site and Off-Site Bound States of the Discrete Nonlinear Schrödinger Equation and the Peierls-Nabarro Barrier
• Dissipative localised structures for the complex Discrete Ginzburg-Landau equation
• Exciting extreme events in the damped and AC-driven NLS equation through plane wave initial conditions
• Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient
• Onset of Identical Synchronization in the Spatial Evolution of Optical Power in a Waveguide Coupler