On an elliptic equation related to the blow-up phenomenon in the nonlinear Schrödinger equation

DOI10.1017/S030821050003095XzbMath0788.35041OpenAlexW2089380413MaRDI QIDQ4277231

Xing-Bin Pan, Russell A. Johnson

Publication date: 6 June 1994

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s030821050003095x

zbMATH Keywords

nonlinear Schrödinger equationblow-up solutionscritical and supercritical cases

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Schrödinger operator, Schrödinger equation (35J10)

Related Items (11)

Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity. II: Supercritical blow-up profiles ⋮ LINEAR VS. NONLINEAR EFFECTS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL ⋮ Singular solutions of the subcritical nonlinear Schrödinger equation ⋮ Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations ⋮ New singular solutions of the nonlinear Schrödinger equation ⋮ Theory of singular vortex solutions of the nonlinear Schrödinger equation ⋮ A survey on asymptotic stability of ground states of nonlinear Schrödinger equations. II ⋮ Transient behavior of collapsing ring solutions in the critical nonlinear Schrödinger equation ⋮ Regular and self-similar solutions of nonlinear Schrödinger equations ⋮ Vortex collapse for the L2-critical nonlinear Schrödinger equation ⋮ Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

Cites Work

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• Focusing and multi-focusing solutions of the nonlinear Schrödinger equation
• Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
• Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
• Uniqueness of non-negative solutions of semilinear equations in \({\mathbb{R}}^ n\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Existence of solitary waves in higher dimensions
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Limit of the solution of a nonlinear Schrödinger equation at blow-up time
• Rate of L2 concentration of blow-up solutions for the nonlinear schrödinger equation with critical power
• The Role of Critical Exponents in Blowup Theorems
• On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations
• Nonexistence theorems for singular solutions of quasilinear partial differential equations
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations

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