27 citations · 103 across the 17 of their papers we have counts for
18 papers
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…
A second-order-in-time scheme for the von Neumann equation with singular self-interaction and simulation of the onset of instability
Agissilaos Athanassoulis, Fotini Karakatsani, Irene Kyza
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In…
Efficient numerical approximations for a non-conservative Nonlinear Schrodinger equation appearing in wind-forced ocean waves
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza
We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy…
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…
A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza +1
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Cr…
Strong solutions for the Alber equation and stability of unidirectional wave spectra
Agissilaos G. Athanassoulis, Gerassimos A. Athanassoulis, Mariya Ptashnyk +1
The Alber equation is a moment equation for the nonlinear Schrödinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea st…
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…
Numerical simulations of X-rays Free Electron Lasers (XFEL)
Paolo Antonelli, Agissilaos Athanassoulis, Zhongyi Huang +1
We study a nonlinear Schrödinger equation which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation appears as a first-principles model…
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…
Semiclassical Propagation of Coherent States for the Hartree equation
Agissilaos Athanassoulis, Thierry Paul, Federica Pezzotti +1
In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approxi…
Strong Semiclassical Approximation of Wigner Functions for the Hartree Dynamics
A. Athanassoulis, T. Paul, F. Pezzotti +1
We consider the Wigner equation corresponding to a nonlinear Schroedinger evolution of the Hartree type in the semiclassical limit . Under appropriate assumptions on th…
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…