In this paper we propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based taking advantage Zakharov equation for one-dimensional which can be written in form so-called compact equations. We generalize these equations case waves. As a test our models, perform numerical simulations ...

We describe completely the dynamics of two Einstein–Friedmann cosmological models, which can be characterized by Hamiltonians $$\begin{aligned} H = \frac{1}{2} (p_{y}^2 - p_{x}^2) + e^{2 x} V(y), \end{aligned}$$with potentials \(V(y)=e^{\lambda y}\), or \(V(y)=(a+by)e^{y}\) with \(\lambda a b\ne 0\).