3 papers
math.NA2025
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…
math.NA2024
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…
math.AP2023
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…