In this talk I shall report about some results obtained together with R. Carles (Montpellier) and C. Sparber (Chicago) on non-linear Schrödinger equations with a non-linear damping term. Such equations are used in non-linear optics, where the damping term models multi-photon absorption, and in Bose-Einstein condensation, when the gas has a negative scattering length and the damping is interpreted as a three-body recombination term. In general a (small) non-linear damping term is used to describe the solution to a NLS equation after the blow-up time and can be seen as a method to continue the solution after that time. I will introduce the main tools used in the analysis and describe the properties of the solutions for this class of equations.
On a class of non-linear Schrödinger equations with non-linear damping
Research Group:
Speaker:
Paolo Antonelli
Institution:
Gran Sasso Science Institute, L'Aquila
Schedule:
Thursday, November 6, 2014 - 16:30 to 17:30
Location:
A-136
Abstract: