Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 023, 15 pages      arXiv:1801.07312      https://doi.org/10.3842/SIGMA.2018.023

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

Anatolij K. Prykarpatski ab
a) The Department of Physics, Mathematics and Computer Science, Cracow University of Technology, Kraków 30-155, Poland
b) Ivan Franko State Pedagogical University of Drohobych, Lviv Region, Ukraine

Received January 22, 2018, in final form February 28, 2018; Published online March 16, 2018

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.

Key words: covering jet manifold; linearization; Hamilton-Jacobi equations; Lax-Sato representation; ABC equation; Gibbons-Tsarev equation; Manakov-Santini equation; contact geometry; differential Toda singular manifold equations.

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