Occurrence and Evolution of Gaussian-Type Soliton-Like Waves in An Open Water Channel

Abstract

The possibility of a transition from the nonlinear equations of impulse, continuity and the complex velocity potential of an inviscid liquid to the nonlinear Schrodinger equation with logarithmic nonlinearity is shown. The solution to this equation in an open water channel is a solitary wave, the shape of which is described by Gauss's law. This wave is not a soliton due to the significant excess of the effects of the nonlinearity of the equations of hydrodynamics over the phenomenon of dispersion. The further evolution of the solitary wave under the examined conditions leads to an increase in the steepness of forward front of the wave, the appearance of a rupture surface and the overturning of the solitary wave. The calculation of these phenomena is presented.