Strong Instability of Ground States to a Fourth Order Schrödinger Equation

DOI10.1093/imrn/rnx273zbMath1462.35347arXiv1703.07977OpenAlexW2606364494MaRDI QIDQ5855193

Denis Bonheure, Tian-Xiang Gou, Louis Jeanjean, Jean-Baptiste Castéras

Publication date: 15 March 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.07977

zbMATH Keywords

stabilitywaveguidesstanding wavesbiharmonic nonlinear Schrödinger equationblow-up in finite/infinite time

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Antennas, waveguides in optics and electromagnetic theory (78A50) Blow-up in context of PDEs (35B44)

Related Items (13)

Non-homogeneous Gagliardo-Nirenberg inequalities in \(\mathbb{R}^N\) and application to a biharmonic non-linear Schrödinger equation ⋮ Non-radial finite time blow-up for the fourth-order nonlinear Schrödinger equations ⋮ The existence and stability of normalized solutions for a bi-harmonic nonlinear Schrödinger equation with mixed dispersion ⋮ Normalized solutions for the mixed dispersion nonlinear Schrödinger equations with four types of potentials and mass subcritical growth ⋮ Normalized solutions for a fourth-order Schrödinger equation with a positive second-order dispersion coefficient ⋮ Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations ⋮ Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions ⋮ Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation ⋮ Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime ⋮ On a fourth‐order nonlinear Helmholtz equation ⋮ Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth ⋮ On the standing waves for the X-ray free electron laser Schrödinger equation ⋮ Radial and non-radial multiple solutions to a general mixed dispersion NLS equation

Cites Work

• Unnamed Item
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• The focusing energy-critical fourth-order Schrödinger equation with radial data
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• Contributions to nonlinear elliptic equations and systems. A tribute to Djairo Guedes de Figueiredo on the occasion of his 80th birthday
• Singular solutions of theL²-supercritical biharmonic nonlinear Schrödinger equation
• Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation
• Self-Focusing with Fourth-Order Dispersion
• The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
• A Note on Berestycki-Cazenave's Classical Instability Result for Nonlinear Schrödinger Equations
• Stability and instability results for standing waves of quasi-linear Schrödinger equations
• Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation
• Dispersion estimates for fourth order Schrödinger equations
• Blowup for Biharmonic NLS
• Singular Solutions of the Biharmonic Nonlinear Schrödinger Equation

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