Advances in Differential Equations
- Adv. Differential Equations
- Volume 15, Number 3/4 (2010), 315-348.
Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential
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.
Adv. Differential Equations Volume 15, Number 3/4 (2010), 315-348.
First available in Project Euclid: 18 December 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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