Unstable gap solitons in inhomogeneous nonlinear Schrödinger equations

DOI10.1016/J.JDE.2012.04.010zbMath1278.35231arXiv1201.2863OpenAlexW2152932105WikidataQ57936717 ScholiaQ57936717MaRDI QIDQ436287

J. Herrera, H. S. Yoon

Publication date: 20 July 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.2863

zbMATH Keywords

gap solitonphase-space methodtopological argument

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Applications of operator theory to differential and integral equations (47N20) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Soliton solutions (35C08)

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Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ An instability criterion for nonlinear standing waves on nonzero backgrounds ⋮ Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model ⋮ A Geometric Approach to Stationary Defect Solutions in One Space Dimension ⋮ Stability of fronts in inhomogeneous wave equations

Cites Work

• Unnamed Item
• Unnamed Item
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• Quantitative measurement of variational approximations
• Emergent nonlinear phenomena in Bose-Einstein condensates. Theory and experiment
• The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives
• The Maslov index for paths
• Stability of discrete solitons in nonlinear Schrödinger lattices
• Optical gap solitons: Past, present, and future; theory and experiments
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Families of Surface Gap Solitons and Their Stability via the Numerical Evans Function Method
• Moving gap solitons in periodic potentials
• Surface Gap Solitons at a Nonlinearity Interface
• Instability of standing waves for non-linear Schrödinger-type equations
• Localized standing waves in inhomogeneous Schrödinger equations
• Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
• Nonlinear propagation of light in one-dimensional periodic structures

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