Microlocal partition of energy for linear wave or Schrödinger equations

Our goal here is to show that one may construct periodic solutions of non-linear Schrödinger equations (for large sets of frequencies), using just a standard iterative scheme instead

Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schr¨ odinger equation in the radial case.. Kenig and

The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for

It is shown that plane wave solutions to the cubic nonlinear Schr¨ odinger equa- tion on a torus behave orbitally stable under generic perturbations of the initial data that are

Abstract: This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials..

Once more the ground states appear to be stable (also for Gaussian perturbations not shown here), but the final state will be only fully reached at longer times (the fitted value of

These remarks being done, in view of defining a uniform optimal design problem for the observability of wave or Schr¨odinger equations, it is natural to raise the problem of

Let us mention that in the nonlinear situation, results exist concerning the long-time behaviour of splitting scheme applied to the nonlinear Schr¨ odinger equation: see the