On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems

In this letter I analyze a covering jet manifold scheme, its relation to the invariant theory of the associated vector fields, and applications to the Lax–Sato-type integrability of nonlinear dispersionless differential systems. The related contact geometry linearization covering scheme is also discussed. The devised techniques are demonstrated for such nonlinear Lax–Sato integrable equations as Gibbons–Tsarev, ABC, Manakov–Santini and the differential Toda singular manifold equations.