Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement
Scattering for the nonlinear Schrödinger equation with a general one-dimensional confinement
We consider the defocusing nonlinear Schrödinger equation in several space dimensions in the presence of an external potential depending on only one space variable. This potential is bounded from below and may grow arbitrarily fast at infinity. We prove existence and uniqueness in the associated Cauchy problem, in a suitable …