4 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…
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…
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…