We describe the relation between operators of invariant differentiation and invariant operators on orbits of Lie group actions. We propose a new effective method for finding differential invariants and operators of invariant differentiation and present examples.

We construct the general and N -soliton solutions of an integro-differential Schrödinger equation with a nonlocal nonlinearity. We consider integrable nonlinear integro-differential equations on the manifold of an arbitrary connected unimodular Lie group. To reduce the equations on the group to equations with a smaller number of independent variables, we use the method of orbits in the coadjoint representation and the generalized harmonic analysis based on it. We demonstrate the capacities of the algorithm with the example of the SO(3) group.

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