Advances in Differential Equations

Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential

Alessandro Selvitella

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Abstract

In this paper we study the dynamics in the semiclassical limit of some classes of solutions for an energy-subcritical focusing nonlinear Schrödinger equation in the presence of an electric potential. We prove the existence of a symmetric configuration of two solitons rotating around a common pole. The existence of such solutions derives mainly from the balance between the attracting force of the two solitons and the centrifugal force due to the rotation and not from the trapping effect of the potential.

Article information

Source
Adv. Differential Equations Volume 15, Number 3/4 (2010), 315-348.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854752

Mathematical Reviews number (MathSciNet)
MR2588772

Subjects
Primary: 35B10: Periodic solutions 35Q40: PDEs in connection with quantum mechanics 35Q41: Time-dependent Schrödinger equations, Dirac equations 35Q51: Soliton-like equations [See also 37K40] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Selvitella, Alessandro. Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential. Adv. Differential Equations 15 (2010), no. 3/4, 315--348. https://projecteuclid.org/euclid.ade/1355854752.


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