Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation

DOI10.1137/17M1154138zbMath1404.35403arXiv1710.09775MaRDI QIDQ4686636

Jean-Baptiste Castéras, Denis Bonheure, Ederson Moreira dos Santos, Robson Nascimento

Publication date: 4 October 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.09775

zbMATH Keywords

orbital stabilityfourth order Schrödinger equationnormalized solution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Higher-order elliptic equations (35J30)

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Cites Work

• Unnamed Item
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• Sobolev spaces of symmetric functions and applications
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
• Proprietà di alcune classi di funzioni in più variabili
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• 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
• The cubic fourth-order Schrödinger equation
• Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case
• Lectures on the orbital stability of standing waves and application to the nonlinear Schrödinger equation
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Global uniqueness of homoclinic orbits for a class of fourth order equations
• Comparison results for solutions of elliptic problems via symmetrization
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Symmetry results for semilinear elliptic systems in the whole space
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• Infinitely many large amplitude homoclinic orbits for a class of autonomous Hamiltonian systems
• Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
• Sharp nonexistence results of prescribed \(L^2\)-norm solutions for some class of Schrödinger-Poisson and quasi-linear equations
• Scattering for the focusingL²-supercritical andḢ²-subcritical biharmonic NLS equations
• Scattering theory for the fourth-order Schrödinger equation in low dimensions
• EXISTENCE OF STEADY STATES FOR THE MAXWELL–SCHRÖDINGER–POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION–COMPACTNESS PRINCIPLE
• THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS
• Self-Focusing with Fourth-Order Dispersion
• The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
• Evolution theorem for a class of perturbed envelope soliton solutions
• Spectra of Linearized Operators for NLS Solitary Waves
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Positivity Properties and Stability of Solitary–Wave Solutions of Model Equations For Long Waves
• Uniqueness of positive radial solutions of semilinear elliptic equations in R^Nand séré's non—degeneracy condition
• Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods
• Dispersion estimates for fourth order Schrödinger equations
• Blowup for Biharmonic NLS
• EXPONENTIAL DECAY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS
• Ground state and non-ground state solutions of some strongly coupled elliptic systems
• Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion
• Strong Instability of Ground States to a Fourth Order Schrödinger Equation