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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].

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
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