Numerical solution of the equations for spatial nonlinear steady-state traveling waves on the free surfaces of homogeneous and two-layer bodies of water

This study is devoted to the construction of some numerical solutions to the previously proposed model equations for three-dimensional disturbances of a small but finite amplitude in liquids of a constant depth. The forms of progressive steady-state waves (both periodic in two horizontal coordinates and solitary) are demonstrated. In a homogeneous liquid, these forms depend on the magnitudes and directions of the wave vectors, whereas, in bodies of water with a small density jump, they also depend on the ratio of layer depths.