Generalized Kadomtsev–Petviashvili equation with an infinite-dimensional symmetry algebra

A generalized Kadomtsev–Petviashvili equation, describing water waves in oceans of varying depth, density and vorticity is discussed. A priori, it involves 9 arbitrary functions of one, or two variables. The conditions are determined under which the equation allows an infinite-dimensional symmetry algebra. This algebra can involve up to three arbitrary functions of time. It depends on precisely three such functions if and only if it is completely integrable.  2002 Elsevier Science (USA). All rights reserved.