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

Abstract

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.

References in corpus (5)

• Remarks on Contact and Jacobi Geometry
• Infinitely many nonlocal conservation laws for the $ABC$ equation with $A+B+C\ne 0$
• The integrable heavenly type equations and their Lie-algebraic structure
• Integrability properties of some symmetry reductions
• Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property

Cited by in corpus (1)

• On the Geometry of Twisted Symmetries: Gauging and Coverings