Nonlinear propagation

[aronroland]

Is your feature request related to a problem? Please describe.
It is well known that the wave group velocities are a function of the wave amplitude when ursell number and the wave height to water depth ration leave the region of applicability of the Airy theory (e.g. Le Méhauté's diagram). Unification of the various theories (Stokes n-th order up to Cnodial theory) was done by Rienecker & Fenton by generalization of the of the wave kinematics based on finite fourier expansion that are solved by applying of the Newton method for the set of nonlinear equations. Based on the given literature a simple approximation for each single component of the amplitude spectra, neglecting the nonlinear interactions among them (e.g. https://www.researchgate.net/publication/328999934_Nonlinear_dispersion_for_ocean_surface_waves) should be implemented to evaluate the influence of nonlinear propagation in practical application on the solution of the wave action balance equation. The work is largely motivated by the work of Marten Dingemanns & Michael Stiassnie. We feel encouraged to replace the simple equation of cg with a nonlinear equation for the wave group veliocites that takes into account the amplitude dispersion of each single wave component itself as a starting point.

Describe the solution you'd like
Cg depends on the wave amplitude

Describe alternatives you've considered
The alterntive solution would be the implementation of the Zakharov equation as suggested by Stuhlmayer & Stiassnie https://www.researchgate.net/publication/349788486_Deterministic_wave_forecasting_with_the_Zakharov_equation?_sg%5B0%5D=soSaLAcM1v2b0o9SJrkFLbe4GqiXtywyEpUDumqA4al3Hx2wpbHogZ5YV5RQJ6bzHI8zl6ha5eAE8LXQvv7h3zHjCPbEnE3z_bEh1sOt.A0FjTdRJuT8wH47ZHC4xwAnyO4WPSkAUAheuIb69T_7ILLWc_7v0irQlFMeY8u93qVPhXh9sgJqJAwl_WrvbAw. However, beeing aware of the computational demands it is at this time still out of the scope in terms of practical applications but it would be great to have a implementation no matter of the computational demands.

Additional context
See related literature