We study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.

VL - 74 UR - http://www.sciencedirect.com/science/article/pii/S0362546X10007613 ER - TY - JOUR T1 - Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential JF - Adv. Differential Equations Y1 - 2010 A1 - Alessandro Selvitella PB - Khayyam Publishing, Inc. VL - 15 UR - https://projecteuclid.org:443/euclid.ade/1355854752 ER - TY - JOUR T1 - Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields JF - Journal of Differential Equations Y1 - 2008 A1 - Alessandro Selvitella AB -In this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

VL - 245 UR - http://www.sciencedirect.com/science/article/pii/S002203960800243X ER -