Remarks on the Schrödinger Equation

Remarks on Fundamental Solutions to Schrödinger Equation with Variable Coefficients

Remarks on a paper by Cordero and Nicola on Feichtinger’s Wiener amalgam spaces and the Schrödinger equation

We derive some consequences of very recent results of Cordero and Nicola on the metaplectic representation, the Wiener amalgam spaces, (whose definition is due to Feichtinger), and their applications to the regularity of the solutions of Schrödinger equation with quadratic Weyl symbol. We do not however discuss the validity of Cordero and Nicola’s claims.

Remarks on the controllability of the Schrödinger equation

In this paper we present some results on the controllability of the Schrödinger equation. We first discuss the controllability of the linear equation with a control distributed along a subdomain or subset of the boundary of the domain where the equation holds. We also analyze some possible extensions to semilinear equations in which the nonlinearity involves the state equation but the control e...

Remarks on the Blow-up for the Schrödinger Equation with Critical Mass on a Plane Domain

Abstract. In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than (T − t), the expected one. Moreover,...

Remarks on the nonlinear Schrödinger equation with harmonic potential

Bose-Einstein condensation is usually modeled by nonlinear Schrödinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrödinger equation. With...