[en] Representation of zero curvature for the system of essentially nonlinear partial differential equations xsub(α,z anti z)=exp(Σsup(r)sub(β=1)ksub(αβ)xsub(β)), 1<=α<=r, with an arbitrary numeral matrix k is constructed in an explicit form. On the base of this representation an invariant integration method for the system when k coincides with the Cartan matrix of simple Lie algebra of rank r is given. The final solutions depend on 2r arbitrary functions