ON THE STUDY OF NONLINEAR INTEGRABLE SYSTEMS IN (2-DIMENSIONS BY DRINFELD-SOKOLOV METHOD(1))

The Drinfeld-Sokolov formalism is extended to the case of operator-val ued affine Lie algebra to derive nonlinear integrable dynamical system s in (2 + 1) dimensions. The Poisson structure of these integrable equ ations are also worked out. While from the first- and second-order flo ws we get some new integrable equations in (2 + 1) dimensions, the KP equation is seen to result from the third-order flow. Complete integra bility of such equations and the existence of the bi-Hamiltonian struc ture are demonstrated.