Perturbations of One - Dimensional Schr

On Local Perturbations of Schr¨odinger Operator on Plane

We obtain necessary and sufficient conditions for emerging of small eigen-value for Schrödinger operator on plane under local operator perturbations. In the case the eigenvalue emerges we construct its asymptotics. The examples are given.

Factorization of Scattering Matrices Due to Partitioning of Potentials in One-dimensional Schr Odinger-type Equations

The one-dimensional Schrodinger equation and two of its generalizations are considered, as they arise in quantum mechanics, wave propagation in a nonhomogeneous medium, and wave propagation in a nonconservative medium where energy may be absorbed or generated. Generically, the zero-energy transmission coe cient vanishes when the potential is nontrivial, but in the exceptional case this coe cie...

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 ...

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

پایداری حلهای منفرد معادله غیر خطی شرودینگر مرتبه پنجم

Analytical investigation of the stability of solitary solutions to the Cubic-Quintic Nonlinear Schr ö dinger Equation (CQNLSE), which governs the propagation of electromagnetic fields in nonlinear fibers, is the main subject of this article. Assuming a perturbation of the form  in the solutions and using the theory of operators, we show that for CQNLSE , is pure imaginary so that such perturbat...