Propagation of Nonlinear Surface Gravity Waves on the Basis of a Model Degenerated in the Parameter of Dispersion

Abstract

We obtain equations generalizing the previously known results on the propagation of nonlinear waves in water of variable depth. To this end, we use the method of power series, which enables us to decrease the dimensionality of the problem and asymptotically construct some weakly dispersive but strongly nonlinear models close to the hyperbolic models of propagation of waves on water. The model has a broader range of application as compared with the available experimental and numerical results.