Linearly degenerate hierarchies of quasiclassical SDYM type

TL;DR

This paper explores the reduction of self-dual Yang-Mills equations to a hierarchy related to one-dimensional vector fields, introducing new mathematical structures and extending the framework to multiple dimensions.

Contribution

It introduces a novel reduction of SDYM equations within linearly degenerate hierarchies, along with wave functions, generating relations, and a dressing scheme, expanding the multidimensional understanding.

Findings

Reduction of SDYM equations to linearly degenerate hierarchies.

Development of wave functions and Lax-Sato equations for the hierarchy.

Extension of the hierarchy framework to multidimensional cases.

Abstract

We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions, introduce generating relation, Lax-Sato equations and the dressing scheme for the reduced hierarchy. Multidimensional case is also discussed.