Family of modified-contracted Schrödinger equations

Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space

We study the long time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short range and long range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of ...

Open-shell energies and two-electron reduced density matrices from the anti-Hermitian contracted Schrödinger equation: A spin- coupled approach

Subcritical Scattering for Defocusing Nonlinear Schrödinger Equations

We survey some known results concerning the asymptotic behavior of solutions to defocusing nonlinear Schrödinger equations. In particular, we discuss the H1 scattering theory for intercritical NLS, as well as the scattering theory in weighted spaces for the mass-subcritical case. We also discuss an instance of modified scattering in the long-range case.

Semiclassical Singularity Propagation Property for Schrödinger Equations

Abstract We consider Schrödinger equations with variable coefficients, and it is supposed to be a long-range type perturbation of the flat Laplacian on Rn. We characterize the wave front set of solutions to Schrödinger equations in terms of the initial state. Then it is shown that the singularity propagates following the classical flow, and it is formulated in a semiclassical setting. Methods a...

Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on R

We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori Lt,x spacetime control on solutions.