Abstract
Several new mathematical models yielding qualitatively correct description of the dynamics of nonlinear sea waves on inhomogeneous flows have been proposed. These models are characterized by a more or less approximated form of the four-wave interaction coefficient as compared to the standard Zakharov equation. The new systems are quite efficient for numerical calculations, although poor in taking into account the details of nonlinearity. The propagation of waves on a jet counterflow, which serves as a waveguide and prevents nonlinear defocusing of waves in the transverse direction, thus creating favorable conditions for the development of modulation instability and the formation of rogue waves, has been simulated as an example.
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