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Global solutions for the Alber equation in
Agissilaos Athanassoulis
The Alber equation is the mixed-state nonlinear Schrödinger equation with singular (-interaction) kernel. It is used in the modeling of stochastic ocean waves, where it appears…
Modulation instability and convergence of the random phase approximation for stochastic sea states
Agissilaos G. Athanassoulis, Irene Kyza
The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial co…
Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas
Agissilaos Athanassoulis, Odin Gramstad
The Alber equation is a phase-averaged second-moment model for the statistics of a sea state, which recently has been attracting renewed attention. We extend it in two ways: firstl…
Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations
Agissilaos Athanassoulis
We consider the semiclassical limit of nonlinear Schrödinger equations with wavepacket initial data. We recover the Wigner measure of the problem, a macroscopic phase-space density…
Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza
Semiclassical asymptotics for linear Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of att…
On the selection of the classical limit for potentials with BV derivatives
Agissilaos Athanassoulis, Thierry Paul
We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove th…
Strong and weak semiclassical limits for some rough Hamiltonians
Agissilaos Athanassoulis, Thierry Paul
We present several results concerning the semiclassical limit of the time dependent Schrödinger equation with potentials whose regularity doesn't guarantee the uniqueness of the un…
Smoothed Affine Wigner Transform
Agissilaos Athanassoulis, Thierry Paul
We study a generalization of Husimi function in the context of wavelets. This leads to a nonnegative density on phase-space for which we compute the evolution equation correspondin…
Strong phase-space semiclassical asymptotics
Agissilaos Athanassoulis, Thierry Paul
Wigner and Husimi transforms have long been used for the phase-space reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of t…
Coarse-scale representations and smoothed Wigner transforms
Agissilaos G. Athanassoulis, Norbert J. Mauser, Thierry Paul
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenizati…
Smoothed Wigner transforms in the numerical simulation of semiclassical (high-frequency) wave propagation
Agissilaos G. Athanassoulis
The numerical simulation of wave propagation in semiclassical (high-frequency) problems is well known to pose a formidable challenge. In this work, a new phase-space approach for t…