Finite time blowup for the nonlinear Schrödinger equation with a delta potential

被引：0

作者：

Hauser, Brandon ^{[1
]}

Holmes, John ^{[1
]}

O'Keefe, Eoghan ^{[1
]}

Raynor, Sarah ^{[1
]}

Yu, Chuanyang ^{[1
]}

机构：

[1] Wake Forest Univ, Dept Math & Stat, Winston Salem, NC 27109 USA

来源：

INVOLVE, A JOURNAL OF MATHEMATICS | 2023年 / 16卷 / 04期

关键词：

well-posedness; initial value problem; Schrodinger equation; NLS; Cauchy problem; Sobolev spaces;

D O I：

10.2140/involve.2023.16.591

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cauchy problem for the nonlinear Schrodinger equation with a delta potential, which can be written as iut + Au + (|u|2 sigma + c8)u = 0. We show that under certain conditions, the L infinity norm of the solution tends to infinity in finite time. In order to prove this, we study the associated Lagrangian and Hamil-tonian, and derive an estimate of the associated variance. We also derive several con-servation laws which a classical solution of the Cauchy problem must also satisfy.

引用

页码：591 / 604

页数：16

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