Integrable equations in (2+1) dimensions associated with symmetric and homogeneous spaces

Abstract

Generalizations of the N-wave, Davey–Stewartson, and Kadomtsev–Petviashvili equations associated with homogeneous and symmetric spaces are presented. These equations are (2+1)-dimensional generalizations of those presented by Fordy and Kulish [Commun. Math. Phys. 89, 427 (1983)] and Athorne and Fordy [J. Phys. A, 20, 1377 (1987)]. Examples are explicitly presented that are associated with the simplest spaces. In particular, a new single component, (2+1)-dimensional generalization of the KdV equation is presented.