Abstract
The Kadomtsev-Petviashvili equation is obtained from the Euler equation in the shallow water, long wave and almost-one- dimensional approximation. In this Letter we consider the case when the almost-one-dimensional approximation is dropped. In such a case we find either a cylindrical Korteweg-de Vries (KdV) equation, if no azimuthal velocity is present, or a (2+1)- dimensional KdV equation. The Cauchy problem for the (2+1)-dimensional KdV equation is solved in terms of that of the (1+1)-dimensional KdV. All calculations are performed in the case of a stratified flow over a flat bottom.
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