RT Journal Article
T1 On a nonlinear Schrodinger equation with a localizing effect
A1 Díaz Díaz, Jesús Ildefonso
A1 Begout, Pascal
AB We consider the nonlinear Schrodinger equation associated to a singular potential of the form a vertical bar u vertical bar(-(1-m))u + bu, for some In is an element of (0, 1), on a possible unbounded domain. We use some suitable energy methods to prove that if Re(a) + Im(a) > 0 and if the initial and right hand side data have compact support then any possible solution must also have a compact support for any t > 0. This property contrasts with the behavior of solutions associated to regular potentials (m >= 1). Related results are proved also for the associated stationary problem and for self-similar Solution on the whole space and potential a vertical bar u vertical bar(-(1-m)u). The existence of solutions is obtained by some compactness methods under additional conditions.
PB Elsevier
SN 1631-073X
YR 2006
FD 2006-04-01
LK https://hdl.handle.net/20.500.14352/49968
UL https://hdl.handle.net/20.500.14352/49968
LA eng
NO EC
NO DGISGPI (Spain).
DS Docta Complutense
RD 18 abr 2025