# Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold

@inproceedings{Ardila2021BlowupAS,
title={Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold},
author={Alex H. Ardila},
year={2021}
}

## References

SHOWING 1-10 OF 25 REFERENCES

### Scattering for the 𝐿² supercritical point NLS

• Mathematics
• 2019
We consider the 1D nonlinear Schrodinger equation with focusing point nonlinearity. "Point" means that the pure-power nonlinearity has an inhomogeneous potential and the potential is the delta

### Mass-energy threshold dynamics for dipolar quantum gases

• Mathematics, Physics
Communications in Mathematical Sciences
• 2022
We consider a Gross-Pitaevskii equation which appears as a model in the description of dipolar Bose-Einstein condensates, without a confining external trapping potential. We describe the asymptotic

### Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation

• Mathematics, Physics
• 2014
We study the focusing nonlinear Schrödinger equation $${i\partial_t u +\Delta u + |u|^{p-1}u=0}$$i∂tu+Δu+|u|p-1u=0, $${x \in \mathbb{R}^N}$$x∈RN in the L2-supercritical regime with finite energy and

### A new proof of scattering below the ground state for the non-radial focusing NLS

• Mathematics
• 2017
We revisit the scattering result of Duyckaerts, Holmer, and Roudenko for the non-radial $\dot H^{1/2}$-critical focusing NLS. By proving an interaction Morawetz inequality, we give a simple proof of

### Global Dynamics below the standing waves for the focusing semilinear Schr\"{o}dinger equation with a repulsive Dirac delta potential

• Mathematics
• 2016
We consider the focusing mass supercritical semilinear Schr\"{o}dinger equation with a repulsive Dirac delta potential on the real line (deltaNLS). Our aim in the present paper is to find a necessary

### Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential

We consider a stationary nonlinear Schrödinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We

### A Class of Nonlinear Schro dinger Equations with Concentrated Nonlinearity

Abstract We consider the nonlinear Schrodinger equation in dimension one with a nonlinearity concentrated in a finite number of points. Detailed results on the local existence of the solution in