By analogy to the Korteweg-de Vries (KdV) equation and its viscous counterpart, the Sajjadi and Smith (SAS) equation, the problem of classical solutions for the Kadomtsev-Petviashvili (KP) equation, for weakly two-dimensional shallow water waves on viscous liquids is considered. The existence and uniqueness, as well as sufficient conditions of solvability, for the nonlinear KP equation is established and discussed.
