The System of Supercompact Equations for Two-Dimensional Waves Propagating on the Surface of a Three-Dimensional Deep Fluid

<p><span>The hydrodynamics of potential flows of a 3D ideal incompressible fluid with a free surface in a gravitational field is considered in the approximation of the Zakharov equation. In the case of one-dimensional waves a special property of the four-wave interaction coefficient in the Zakharov equation allows it to be written in a simple form of the so-called supercompact equations for one-dimensional counterpropagating waves. We generalize the system of equations to the case of</span> two-dimensional surface waves and <span>study the problem of modulation instability for a monochromatic and standing wave, as well as resonant interactions of such waves within the framework of this model.</span> The work was supported by Grant No. 19-72-30028 of the Russian Science Foundation.</p>