On the existence of special solutions of the generalized Davey-Stewartson system

In this note we show that for certain choice of parameters the hyperbolic-elliptic-elliptic generalized Davey-Stewartson system admits time-dependent travelling wave solutions of the kind given in [V.A. Arkadiev, AX Pogrebkov, M.C. Polivanov, Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation, Physica D 36 (1989) 189-197] for the hyperbolic Davey-Stewartson system. These solutions lead to radial solutions as well. We also find the sufficient conditions for non-existence of travelling wave solutions for the hyperbolic-elliptic-elliptic generalized Davey-Stewartson system by using the point of view developed in [A. Eden,T.B. Gurel, E. Kuz, Focusing and defocusing cases of the purely elliptic generalized Davey-Stewartson system, IMA J. Appl. Math. (in press)]. (C) 2009 Elsevier Ltd. All rights reserved.