In this paper we consider the time-independent one-dimensional non linear Schrodinger 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 a, then a non linear real-valued bound state exists. Furthermore, we show that when or is larger than 2 a further new real-valued stationary state appears under some conditions.
Stationary states for non linear one-dimensional Schrodinger equations with singular potential / F. F. G., Della Casa; Sacchetti, Andrea. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - STAMPA. - 219:1(2006), pp. 60-68. [10.1016/j.physd.2006.05.014]
Stationary states for non linear one-dimensional Schrodinger equations with singular potential
SACCHETTI, Andrea
2006
Abstract
In this paper we consider the time-independent one-dimensional non linear Schrodinger 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 a, then a non linear real-valued bound state exists. Furthermore, we show that when or is larger than 2 a further new real-valued stationary state appears under some conditions.
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