We consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in a finite number of points. Detailed results on the local existence of the solution in fractional Sobolev spaces Hρare given. We also prove the conservation of the L2-norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space H1Finally we prove the existence of blow-up solutions for strongly attractive interaction. © 2001 Academic Press.
Adami, R., Teta, A. (2001). A class of nonlinear Schrodinger equations with concentrated nonlinearity. JOURNAL OF FUNCTIONAL ANALYSIS, 180(1), 148-175 [10.1006/jfan.2000.3697].
A class of nonlinear Schrodinger equations with concentrated nonlinearity
ADAMI, RICCARDO;
2001
Abstract
We consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in a finite number of points. Detailed results on the local existence of the solution in fractional Sobolev spaces Hρare given. We also prove the conservation of the L2-norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space H1Finally we prove the existence of blow-up solutions for strongly attractive interaction. © 2001 Academic Press.
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