SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2009-2010
Jeudi 18 mars 2010 :
Yoshio TSUTSUMI
(Univ. Kyoto, Japon)
Existence of cavity soliton for the nonlinear Schrödinger equation with damping and homogeneous forcing terms
We consider the existence of stationary solution for the Lugiato-Lefever equation on Euclidean spaces of dimensions less than or equal to three, to which is referred as (LL).
The (LL) equation is a nonlinear Schrödinger equation with damping and homogeneous forcing terms, which describes a physical model of a unidirectional ring or Fabry-Perot cavity with plane mirrors containing a Kerr medium driven by a coherent plane-wave field.
The stationary solution of (LL) is called a "Cavity Soliton".
There are two difficulties in this problem.
- One is that a forcing term is spatially homogeneous, which implies it does not belong to the square-integrable function sapce.
- Another is that (LL) has no variational structure because of the presence of damping term.
For some region of parameters, we show the existence of stationary solution for (LL).
This is a joing work with T. Miyaji, Y. Miyamoto and I. Ohnishi.
