Blow-up of solutions to cubic nonlinear Schrödinger equations with defect: The radial case

2017 ◽  
Vol 6 (2) ◽  
pp. 183-197 ◽  
Author(s):  
Olivier Goubet ◽  
Emna Hamraoui
Keyword(s):  
Blow Up ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Radial Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Radial Case ◽  
Nonlinear Schrodinger Equations ◽  
Dimension 2

AbstractIn this article we investigate both numerically and theoretically the influence of a defect on the blow-up of radial solutions to a cubic NLS equation in dimension 2.

Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials

2006 ◽  
Vol 136 (5) ◽  
pp. 889-907 ◽  
Author(s):  
A. Ambrosetti ◽  
D. Ruiz
Keyword(s):  
Perturbation Technique ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Radial Solutions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Image Position ◽  
Vanishing Potentials

We prove the existence of radial solutions of concentrating on a sphere for potentials which might be zero and might decay to zero at infinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov–Schmidt reduction.

On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth

2021 ◽  
Author(s):  
Amin Esfahani
Keyword(s):  
Blow Up ◽  
Dynamical Behavior ◽  
Critical Growth ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Quadratic Interaction ◽  
Nonlinear Schrodinger Equations ◽  
Normalized Solutions

In this paper, we study the dynamical behavior of solutions of nonlinear Schrödinger equations with quadratic interaction and [Formula: see text]-critical growth. We give sharp conditions under which the existence of global and blow-up solutions are deduced. We also show the existence, stability, and blow-up behavior of normalized solutions of this system.

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