Gauge covariant formulation of the generating operator. 2. Systems on homogeneous spaces

A gauge covariant approach to the operator Λ, generating the n-wave type equations on homogeneous spaces is proposed. The operator Λ̃ for the gauge equivalent equations is explicitly constructed. The main results (such as conservation laws, hierarchies of hamiltonian structures, etc.) for the n-wave type equations and their gauge equivalent ones are formulated in terms of Λ and Λ̃ respectively.