Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications
Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications
We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and powerlike nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no …