Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17, 1 issue

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
Finite time blowup for the nonlinear Schrödinger equation with a delta potential

Brandon Hauser, John Holmes, Eoghan O’Keefe, Sarah Raynor and Chuanyang Yu

Vol. 16 (2023), No. 4, 591–604
Abstract

We study the Cauchy problem for the nonlinear Schrödinger equation with a delta potential, which can be written as

iut + Δu + (|u|2σ + cδ)u = 0.

We show that under certain conditions, the L norm of the solution tends to infinity in finite time. In order to prove this, we study the associated Lagrangian and Hamiltonian, and derive an estimate of the associated variance. We also derive several conservation laws which a classical solution of the Cauchy problem must also satisfy.

Keywords
well-posedness, initial value problem, Schrödinger equation, NLS, Cauchy problem, Sobolev spaces
Mathematical Subject Classification
Primary: 35Q41
Milestones
Received: 27 April 2022
Revised: 9 August 2022
Accepted: 12 August 2022
Published: 31 October 2023

Communicated by Martin Bohner
Authors
Brandon Hauser
Department of Mathematics and Statistics
Wake Forest University
Winston Salem, NC
United States
John Holmes
Department of Mathematics and Statistics
Wake Forest University
Winston Salem, NC
United States
Eoghan O’Keefe
Department of Mathematics and Statistics
Wake Forest University
Winston Salem, NC
United States
Sarah Raynor
Department of Mathematics and Statistics
Wake Forest University
Winston Salem, NC
United States
Chuanyang Yu
Department of Mathematics and Statistics
Wake Forest University
Winston Salem, NC
United States