Instability of standing waves for a class of nonlinear Schrödinger equations

DOI10.1016/j.jmaa.2006.04.082zbMath1105.35119OpenAlexW2091931933MaRDI QIDQ860621

Jian Zhang, Ji Shu

Publication date: 9 January 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.04.082

zbMATH Keywords

ground stateglobal existenceblowupnonlinear Schrödinger equationsstanding wave

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

Related Items (6)

Nonlinear Schrödinger equation with combined power-type nonlinearities and harmonic potential ⋮ Global existence and blow-up of solutions for nonlinear Klein-Gordon equation with damping term and nonnegative potentials ⋮ Energy criterion of global existence for energy-critical Schrödinger equations with subcritical perturbations ⋮ Sharp conditions of global existence for second‐order derivative nonlinear Schrödinger equations with combined power‐type nonlinearities ⋮ Blow up threshold for the Gross-Pitaevskii system with combined nonlocal nonlinearities ⋮ On the Cauchy problem for a generalized Boussinesq equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Instability of nonlinear bound states
• An instability mechanism for radially symmetric standing waves of a nonlinear Schrödinger equation
• Blow-up of \(H^ 1\) solution for the nonlinear Schrödinger equation
• Saddle points and instability of nonlinear hyperbolic equations
• Existence of solitary waves in higher dimensions
• On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• On the finite-time behaviour for nonlinear Schrödinger equations
• Stability of standing waves for nonlinear Schrödinger equations with unbounded potentials
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Blow-Up of H 1 Solutions for the One-Dimensional Nonlinear Schrodinger Equations with Critical Power Nonlinearity
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Existence of multi-bumb solutions for nonlinear schrödinger equations via variational method
• Stability of attractive Bose-Einstein condensates
• Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential
• Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations.

This page was built for publication: Instability of standing waves for a class of nonlinear Schrödinger equations