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An Instability Criterion for Nonlinear Standing Waves on Nonzero Backgrounds

https://doi.org/10.1007/s00332-014-9215-8
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Emergent nonlinear phenomena in Bose-Einstein condensates : theory and experiment
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Existence of solutions to the Cauchy problem and stability of kink-solutions of the nonlinear Schrödinger equation
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Stability of the lowest-order mode of a nonlinear wave equation in a cubic medium
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Dark solitons in external potentials
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Lagrangian approach for dark solitons
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Unstable gap solitons in inhomogeneous nonlinear Schrödinger equations
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Frequency characteristics of the dark and bright surface solitons at a nonlinear metamaterial interface
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Quasi 1D Bose–Einstein condensate flow past a nonlinear barrier
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Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons
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Dark optical solitons: physics and applications
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Instability of standing waves for non-linear Schrödinger-type equations
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Stationary solutions to a nonlinear Schrödinger equation with potential in one dimension
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A direct perturbation theory for dark solitons based on a complete set of the squared Jost solutions
inferredcites →https://doi.org/10.1088/0305-4470/32/21/307openalex-snapshot
Foundation of direct perturbation method for dark solitons
inferredcites →https://doi.org/10.1088/0305-4470/38/11/006openalex-snapshot
A perturbation method for dark solitons based on a complete set of the squared Jost solutions
inferredcites →https://doi.org/10.1088/0951-7715/13/1/305openalex-snapshot
Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
inferredcites →https://doi.org/10.1088/0951-7715/20/2/010openalex-snapshot
The black solitons of one-dimensional NLS equations
inferredcites →https://doi.org/10.1088/0951-7715/23/9/002openalex-snapshot
Localized standing waves in inhomogeneous Schrödinger equations
inferredcites →https://doi.org/10.1088/1751-8113/43/21/213001openalex-snapshot
Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
inferredcites →https://doi.org/10.1103/physreva.45.4974openalex-snapshot
Bright and dark surface waves at a nonlinear interface
inferredcites →https://doi.org/10.1103/physreva.46.5999openalex-snapshot
Stability analysis of stationary nonlinear guided waves in self-focusing and self-defocusing Kerr-like layered media
inferredcites →https://doi.org/10.1103/physreva.65.053611openalex-snapshot
Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices
inferredcites →https://doi.org/10.1103/physreve.49.1657openalex-snapshot
Perturbation-induced dynamics of dark solitons
inferredcites →https://doi.org/10.1103/physreve.49.2397openalex-snapshot
Direct perturbation theory for dark solitons
inferredcites →https://doi.org/10.1103/physreve.54.2015openalex-snapshot
Instability-induced dynamics of dark solitons
inferredcites →https://doi.org/10.1103/physreve.55.2835openalex-snapshot
Nonlinear Schrödinger flow past an obstacle in one dimension
inferredcites →https://doi.org/10.1103/physreve.70.066620openalex-snapshot
Perturbation theory for dark solitons: Inverse scattering transform approach and radiative effects
inferredcites →https://doi.org/10.1103/physrevlett.105.050405openalex-snapshot
Submicron Spatial Modulation of an Interatomic Interaction in a Bose-Einstein Condensate
inferredcites →https://doi.org/10.1103/physrevlett.66.1583openalex-snapshot
Spatial dark-soliton stripes and grids in self-defocusing materials
inferredcites →https://doi.org/10.1103/physrevlett.77.1193openalex-snapshot
Stability Criterion for Dark Solitons
inferredcites →https://doi.org/10.1103/physrevlett.83.5198openalex-snapshot
Dark Solitons in Bose-Einstein Condensates
inferredcites →https://doi.org/10.1103/physrevlett.86.3296openalex-snapshot
Self-Focusing and Defocusing in Waveguide Arrays
inferredcites →https://doi.org/10.1103/revmodphys.78.1311openalex-snapshot
Production of cold molecules via magnetically tunable Feshbach resonances
inferredcites →https://doi.org/10.1103/revmodphys.83.247openalex-snapshot
Solitons in nonlinear lattices
inferredcites →https://doi.org/10.1126/science.287.5450.97openalex-snapshot
Generating Solitons by Phase Engineering of a Bose-Einstein Condensate
inferredcites →https://doi.org/10.1142/s0217979205032279openalex-snapshot
DYNAMICS OF BRIGHT MATTER WAVE SOLITONS IN A BOSE–EINSTEIN CONDENSATE
inferredcites →https://doi.org/10.1142/s0217984904006809openalex-snapshot
PATTERN FORMING DYNAMICAL INSTABILITIES OF BOSE–EINSTEIN CONDENSATES
inferredcites →https://doi.org/10.1364/josab.10.001077openalex-snapshot
Stability of bright and dark surface waves
inferredcites →https://doi.org/10.1364/josab.11.000789openalex-snapshot
Stability of stationary dark waves guided by nonlinear surfaces and waveguides
inferredcites →https://doi.org/10.1364/josab.8.000759openalex-snapshot
Stationary fundamental dark surface waves
inferredcites →https://doi.org/10.1364/josab.8.002265openalex-snapshot
Stability analysis of the fundamental dark surface wave
inferredcites →https://doi.org/10.1364/ol.17.000580openalex-snapshot
Gray and dark spatial solitary waves in slab waveguides
inferredcites →https://doi.org/10.1364/ol.20.001527openalex-snapshot
Instabilities of dark solitons
inferredcites →https://doi.org/10.1364/ol.31.002888openalex-snapshot
Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model
inferredcites →https://doi.org/10.57262/ade/1356651683openalex-snapshot
Stability and instability of traveling solitonic bubbles

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4160576openalex-extracted
Flat-Bottom Dark Gap Modes as a New Localized State Supported by Periodic Nanostructures
inferred← citeshttps://doi.org/10.1007/s10440-014-9991-zopenalex-snapshot
Stability of Fronts in Inhomogeneous Wave Equations
inferred← citeshttps://doi.org/10.1016/j.jde.2012.08.007openalex-snapshot
Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneity
inferred← citeshttps://doi.org/10.1098/rsta.2017.0183openalex-snapshot
Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities
inferred← citeshttps://doi.org/10.1137/15m1026742openalex-snapshot
A Geometric Approach to Stationary Defect Solutions in One Space Dimension
inferred← citeshttps://doi.org/10.1137/20m1381319openalex-snapshot
Generalized Maslov Indices for Non-Hamiltonian Systems
inferred← citeshttps://doi.org/10.1137/22m1533797openalex-snapshot
Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation
inferred← citeshttps://doi.org/10.1140/epjd/e2020-10251-0openalex-snapshot
Formation of solitonic bound state via light-matter interaction
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Localised structures in some non-standard, singularly perturbed partial differential equations
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