Nonlinear Schrödinger equation with combined power-type nonlinearities and harmonic potential

DOI10.1007/S10483-010-0412-7zbMath1203.35268OpenAlexW2185171007MaRDI QIDQ605126

Chuang Xu, Run-Zhang Xu

Publication date: 23 November 2010

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-010-0412-7

zbMATH Keywords

nonlinear Schrödinger equationharmonic potentialinvariant manifoldsharp criterioncombined power-type nonlinearities

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (2)

On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term ⋮ Initial boundary value problem for a class of fourth-order wave equation with viscous damping term

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Small solutions to nonlinear Schrödinger equations
• Instability of standing waves for a class of nonlinear Schrödinger equations
• Cauchy problem and Ehrenfest's law of nonlinear Schrödinger equations with potentials
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• On solutions on the initial value problem for the nonlinear Schrödinger equations
• Remarks on convergence of the Feynman path integrals
• Blow-up of \(H^ 1\) solution for the nonlinear Schrödinger equation
• Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\)
• Saddle points and instability of nonlinear hyperbolic equations
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Stability of standing waves for nonlinear Schrödinger equations with unbounded potentials
• Remarks on nonlinear Schrödinger equations with harmonic potential
• Remarks on global existence for the supercritical nonlinear Schrödinger equation with a harmonic potential
• Nonlinear Schrödinger equation with harmonic potential
• 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
• CRITICAL NONLINEAR SCHRÖDINGER EQUATIONS WITH AND WITHOUT HARMONIC POTENTIAL
• The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
• Remarks on nonlinear Schrödinger equation with harmonic potential
• Collapses of Wavefunctions in Multi-Dimensional Nonlinear Schrödinger Equations under Harmonic Potential
• Stability of attractive Bose-Einstein condensates
• Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations.

This page was built for publication: Nonlinear Schrödinger equation with combined power-type nonlinearities and harmonic potential