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arXiv · 1307.6895

On the Schrödinger equation with singular potentials

Jaime Angulo Pava·Lucas C. F. Ferreira
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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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Jaime Angulo Pava, Lucas C. F. Ferreira. 2013-07-25. On the Schrödinger equation with singular potentials. https://arxiv.org/abs/1307.6895

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