We study the Cauchy problem for a system of two coupled nonlinear focusing Schrodinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the data of the problem, are proved; in particular we prove, for suitable values of the parameters, that the blow-up threshold (if the nonlinearity has the critical growth) is a universal constant.
On the blow-up threshold for weakly coupled nonlinear Schrodinger equations / Fanelli, Luca; Montefusco, Eugenio. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - STAMPA. - 40:(2007), pp. 14139-14150. [10.1088/1751-8113/40/47/007]
On the blow-up threshold for weakly coupled nonlinear Schrodinger equations
FANELLI, Luca;MONTEFUSCO, Eugenio
2007
Abstract
We study the Cauchy problem for a system of two coupled nonlinear focusing Schrodinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the data of the problem, are proved; in particular we prove, for suitable values of the parameters, that the blow-up threshold (if the nonlinearity has the critical growth) is a universal constant.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.