Adami, Riccardo; Teta, Alessandro A simple model of concentrated nonlinearity. (English) Zbl 0967.81010 Dittrich, Jaroslav (ed.) et al., Mathematical results in quantum mechanics. QMath7 conference, Prag, Czech Republic, June 22-26, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 108, 183-189 (1999). Summary: We study the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in a point. We give results on local and global existence of the solution and find conditions for the blow-up. In the critical case an explicit blow-up solution is constructed.For the entire collection see [Zbl 0911.00055]. Cited in 9 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q55 NLS equations (nonlinear Schrödinger equations) Keywords:nonlinear Schrödinger equation; dimension one; local and global existence; blow-up PDFBibTeX XMLCite \textit{R. Adami} and \textit{A. Teta}, in: Mathematical results in quantum mechanics. QMath7 conference, Prag, Czech Republic, June 22--26, 1998. Basel: Birkhäuser. 183--189 (1999; Zbl 0967.81010)