Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect
The authors consider a generalization of a cubic nonlinear Schrödinger equation in one space dimension with a point defect, obtained by adding a linear term to the differential operator and the right hand side, containing a delta-function. The problem is discretized in time by the Crank-Nicolson scheme. Different properties of the solution are investigated and in particular the well-possedness of the scheme is established. It is proved that the obtained semi-discrete problem can be considered as a discrete infinite dynamical system with a global attractor. The conditions of compactness and finite dimensionality of this global attractor are established.
scientific article; zbMATH DE number 5907629
scientific article