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Finite time
blowup for the nonlinear Schrödinger equation with a delta
potential
Brandon Hauser, John Holmes, Eoghan O’Keefe, Sarah Raynor and Chuanyang Yu |
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Vol. 16 (2023), No. 4, 591–604
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Abstract |
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We study the Cauchy problem for the nonlinear Schrödinger equation with a delta potential, which can be written as We show that under certain conditions, the 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. |
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Keywords
well-posedness, initial value problem, Schrödinger
equation, NLS, Cauchy problem, Sobolev spaces
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Mathematical Subject Classification
Primary: 35Q41
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Milestones
Received: 27 April 2022
Revised: 9 August 2022
Accepted: 12 August 2022
Published: 31 October 2023
Communicated by Martin Bohner
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Authors |
| Brandon Hauser | |
| Department of Mathematics and
Statistics Wake Forest University Winston Salem, NC United States |
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| John Holmes | |
| Department of Mathematics and
Statistics Wake Forest University Winston Salem, NC United States |
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| Eoghan O’Keefe | |
| Department of Mathematics and
Statistics Wake Forest University Winston Salem, NC United States |
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| Sarah Raynor | |
| Department of Mathematics and
Statistics Wake Forest University Winston Salem, NC United States |
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| Chuanyang Yu | |
| Department of Mathematics and
Statistics Wake Forest University Winston Salem, NC United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
