3 papers
math.AP2026
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 appear…
math.NA2026
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…