- 05-302 Riccardo Adami, Andrea Sacchetti
- The transition from diffusion to blow-up for a nonlinear Schroedinger
equation in dimension 1.
(43K, LATeX 2e)
Sep 2, 05
(auto. generated ps),
of related papers
Abstract. We consider the time-dependent one-dimensional non linear Schroedinger
dinger equation with pointwise singular potential. We prove that, if
the strength of the nonlinear term is small enough, then the solution is
well defined for any time, regardless of the choice of initial data; in
contrast, if the nonlinearity power is larger than a critical
value, for some initial data a blow-up phenomenon occurs in finite time.
In particular, if the system is initially prepared in the ground
state of the linear part of the Hamiltonian, then we
obtain an explicit condition on the parameters for the occurrence of