Stationary states for non linear one-dimensional Schrödinger equations with singular potential

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• 作者：Filippo F.G. Della Casa and Andrea Sacchetti
• 刊名：Physica D
• 出版年：2006
• 期刊代码：55_01672789
• 类别：ph
• 出版时间：1 July 2006
• 卷：219
• 期：1
• 页码：60-68
• 文件大小：402 K

摘要

In this paper we consider the time-independent one-dimensional non linear Schrödinger equation (NLS) with pointwise singular potential. We prove that when the strength of the pointwise interaction is less than a critical value, depending on the nonlinearity power σ, then a non linear real-valued bound state exists. Furthermore, we show that when σ is larger than 2 a further new real-valued stationary state appears under some conditions.