On the Schrödinger equation with singular potentials

2013/07/25 by Pava, Jaime Angulo, Ferreira, Lucas C. F.
#35A05 #35A07 #35B10 #35B40 #35C15 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.6895

Abstract

We study the Cauchy problem for the non-linear Schrödinger equation with singular potentials. For point-mass potential and nonperiodic case, we prove existence and asymptotic stability of global solutions in weak-L^p spaces. Specific interest is give to the point-like δ and δ' impurity and for two δ-interactions in one dimension. We also consider the periodic case which is analyzed in a functional space based on Fourier transform and local-in-time well-posedness is proved.

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