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.

10aBifurcation theory10aNonlinear Schrödinger equations10aStationary solutions1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S0362546X1000761300486nas a2200121 4500008004100000245011700041210006900158260003300227300001400260490000700274100002700281856005600308 2010 eng d00aSemiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential0 aSemiclassical evolution of two rotating solitons for the Nonline bKhayyam Publishing, Inc.c03 a315–3480 v151 aSelvitella, Alessandro uhttps://projecteuclid.org:443/euclid.ade/135585475200988nas a2200133 4500008004100000022001400041245012300055210007000178300001600248490000800264520048400272100002700756856007100783 2008 eng d a0022-039600aAsymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields0 aAsymptotic evolution for the semiclassical nonlinear Schrödinger a2566 - 25840 v2453 aIn 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.

1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S002203960800243X