Water waves can be described by differential equations, more often by nonlinear partial. In this article you can see how those type of equations are derived and solved (application is propagation of long surface waves for tsunami modeling): https://www.researchgate.net/publication/275581998_Evolution_of_long_nonlinear_waves_on_shelves

There are also equations for internal waves. There are many types of waves in the ocean: surface, internal, acoustic, seismic (on the bottom). And all of them can be described by different equations.

Conference Paper Evolution of long nonlinear waves on shelves

Dear Evangelous-Ioannies, I recently added another conference paper on similar topic, with derivation of another perturbation of KdV equation: https://www.researchgate.net/publication/305641177_Interaction_of_a_Solitary_Tsunami_Wave_with_River_Current

But it might be also useful to start from some books about equations for water waves, like: http://www.springer.com/us/book/9789048178391 , https://www.amazon.com/Linear-Nonlinear-Waves-G-Whitham/dp/0471359424

Conference Paper Interaction of a Solitary Tsunami Wave with River Current

Appreciated Dr. Yegorov,

Thank You