Abstract :
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.
