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

TL;DR

This paper explores a geometric linearization technique for integrable nonlinear differential systems, demonstrating its application to various well-known Lax-Sato integrable equations and connecting it to invariant theory and contact geometry.

Contribution

It introduces a covering jet manifold scheme and relates it to invariant theory and contact geometry, providing new tools for analyzing integrability of nonlinear systems.

Findings

Applied the technique to Gibbons-Tsarev, ABC, Manakov-Santini, and Toda equations.

Established connections between covering schemes and invariant theory.

Demonstrated the effectiveness of the approach in analyzing integrable 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.