THE MOYAL BRACKET AND THE DISPERSIONLESS LIMIT OF THE KP HIERARCHY

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. T his Lax equation is closer to that used in the study of the dispersion less KP hierarchy, and is obtained by replacing the Poisson bracket wi th the Moyal bracket. The dispersionless limit, under which the Moyal bracket collapses to the Poisson bracket, is particularly simple.