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A splitting method for the nonlinear Schrödinger equation
We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical well-posedness L2(Rd)-theory. More precisely, we prove that ...
Dispersive Properties for Discrete Schrödinger Equations
In this paper we prove dispersive estimates for the system formed by two coupled discrete Schrödinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting ...
Dispersion for the Schrödinger equation on networks
In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger ...