On the Linearization Covering Technique and Its Application to Integrable Nonlinear Differential Systems - Prykarpatski, A.K. (Symmetry, Integrability and Geometry: Methods and Applications, 2018)
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.