On Local Perturbations of Schr¨odinger Operator on Plane

A Modulation Method for Self-focusing in the Perturbed Critical Nonlinear Schr Odinger Equation

In this Letter we introduce a systematic perturbation method for analyzing the e ect of small perturbations on critical self focusing by reducing the perturbed critical nonlinear Schrodinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simpli ed, depending on whether PNLS is power conserving ...

Absolute Continuity of the Periodicmagnetic Schr Odinger Operatoralexander

We prove that the spectrum of the Schrr odinger operator with periodic electric and magnetic potentials is absolutely continuous.

On Local Perturbations of Shr Odinger Operator in Axis

We adduce the necessary and sufficient condition for arising of eigenvalues of Shrödinger operator in axis under small local perturbations. In the case of eigenvalues arising we construct their asymptotics.

On Absolute Continuity of the Periodic Schr odinger

This paper concerns the Schrr odinger operator ?+V (x) in R d ; d 3, with periodic potential V. Under the assumption V 2 L d=2 loc (R d), it is shown that the spectrum of ?+V (x) is absolutely continuous. The condition on the potential V is optimal in the context of L p spaces.

Hausdorff Dimension of Spectrum of One-dimensional Schr Odinger Operator with Sturmian Potentials