REPRESENTATION OF ZERO CURVATURE FOR THE SYSTEM OF NON-LINEAR PARTIAL-DIFFERENTIAL EQUATIONS XALPHA,ZZ-BAR=EXP(KX)ALPHA AND ITS INTEGRABILITY

Representation of zero curvature for the system of essentially nonlinear partial differential equations {Mathematical expression}, with an arbitrary numeral matrix k is constructed in an explicit form. On the basis of this representation we give an invariant integration method for the system when k coincides with the Cartan matrix of simple Lie algebra of rank r. The final solutions depend on 2 r arbitrary functions. © 1979 D. Reidel Publishing Company.