Abstract
In the theory of nonlinear oscillations and waves with dissipation and dispersion of the medium, it is applied the two-dimensional Korteweg - de Vries equation. In this paper a generalized nonlinear partial differential equation of third order with a cubic stream function is considered. The exact analytical solutions of two-dimensional Korteweg - de Vries equation and Kadomtsev - Petviashvili equation are obtained. The graphs effect of non-linear parameters of medium to the maximum amplitude of the waves is presented.
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