Periodic nonlinear Schrödinger equation with application to photonic crystals

2004/04/25 by А. А. Панков, A. Pankov, Pankov, A. · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Nonlinear Photonic Systems #math-ph #math.AP #math.MP #msc:35Q55 #msc:58E50 #msc:78M30

paper · pdf · doi:10.48550/arxiv.math/0404450

arxiv created 2004/05/05 · arxiv updated 2009/12/01

Abstract

We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schrödinger equations. We also sketch an application to nonlinear optics and discuss some open problems.

Citations

• Traveling Waves in Lattice Dynamical Systems

Cited by

• Ground state solutions to generalized nonlinear wave equations with infinite-dimensional kernel
• Analysis of nonlinear resonances in resonator crystals: Tight-binding approximation and existence of subwavelength soliton-like solutions
• Multi-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions
• Existence of nontrivial solutions for asymptotically linear periodic Schrödinger equations
• A Note on Nonlinear Schr "odinger Equations: Unveiling the Relation\n Between Spectral Gaps and the Nonlinearity Behavior

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