We consider the time-dependent one-dimensional nonlinear Schrödinger equation with a pointwise singular potential. We prove that if the strength of the nonlinear term is small enough, then the solution is well defined for any time, regardless of the choice of initial data; in contrast, if the nonlinearity power is larger than a critical value, for some initial data a blow-up phenomenon occurs in finite time. In particular, if the system is initially prepared in the ground state of the linear part of the Hamiltonian, then we obtain an explicit condition on the parameters for the occurrence of the blow-up. © 2005 IOP Publishing Ltd.

Adami, R., Sacchetti, A. (2005). The transition from diffusion to blow-up for a nonlinear Schrodinger equation in dimension 1. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 38(39), 8379-8392 [10.1088/0305-4470/38/39/006].

The transition from diffusion to blow-up for a nonlinear Schrodinger equation in dimension 1

ADAMI, RICCARDO;
2005

Abstract

We consider the time-dependent one-dimensional nonlinear Schrödinger equation with a pointwise singular potential. We prove that if the strength of the nonlinear term is small enough, then the solution is well defined for any time, regardless of the choice of initial data; in contrast, if the nonlinearity power is larger than a critical value, for some initial data a blow-up phenomenon occurs in finite time. In particular, if the system is initially prepared in the ground state of the linear part of the Hamiltonian, then we obtain an explicit condition on the parameters for the occurrence of the blow-up. © 2005 IOP Publishing Ltd.
Articolo in rivista - Articolo scientifico
Nonlinear Schrodinger equation, diffusion and blow-up
English
2005
38
39
8379
8392
none
Adami, R., Sacchetti, A. (2005). The transition from diffusion to blow-up for a nonlinear Schrodinger equation in dimension 1. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 38(39), 8379-8392 [10.1088/0305-4470/38/39/006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/11569
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