NEW SYMMETRY REDUCTIONS AND EXACT-SOLUTIONS OF THE DAVEY-STEWARTSON SYSTEM .1. REDUCTIONS TO ORDINARY DIFFERENTIAL-EQUATIONS

In this article symmetry reductions and exact solutions are presented for the (2+1)-dimensional Davey-Stewartson (DS) system which has the completely integrable DSI and DSII systems as special cases. These symmetry reductions are obtained using the direct method originally developed by Clarkson and Kruskal to study symmetry reductions of the Boussinesq equation which involves no group theoretic techniques. The DS system is reduced directly to ordinary differential equations, with no intermediate step. Using these reductions exact solutions of the DS system including some expressible in terms of the second and fourth Painleve equations and elementary functions are obtained.