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.

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 1731 - 1737 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X10007613 %R https://doi.org/10.1016/j.na.2010.10.045 %0 Journal Article %J Adv. Differential Equations %D 2010 %T Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential %A Alessandro Selvitella %B Adv. Differential Equations %I Khayyam Publishing, Inc. %V 15 %P 315–348 %8 03 %G eng %U https://projecteuclid.org:443/euclid.ade/1355854752 %0 Journal Article %J Journal of Differential Equations %D 2008 %T Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields %A Alessandro Selvitella %XIn 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.

%B Journal of Differential Equations %V 245 %P 2566 - 2584 %G eng %U http://www.sciencedirect.com/science/article/pii/S002203960800243X %R https://doi.org/10.1016/j.jde.2008.05.012