On the study of nonlinear integrable systems in (2+1) dimensions by Drinfeld-Sokolov method

The Drinfeld-Sokolov formalism is extended to the case of operator-valued affine Lie algebra to derive nonlinear integrable dynamical systems in (2 + 1) dimensions. The Poisson structure of these integrable equations are also worked out. While from the first- and second-order flows we get some new integrable equations in (2 + 1) dimensions, the KP equation is seen to result from the third-order flow. Complete integrability of such equations and the existence of the bi-Hamiltonian structure are demonstrated.