Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets

TL;DR

This paper explores the connections between oriented associativity equations, symmetry consistent conjugate curvilinear coordinate nets, and semi-Hamiltonian hydrodynamic systems, revealing their interrelated structures.

Contribution

It introduces a comprehensive description of the relationships among these mathematical structures, expanding understanding of their interplay.

Findings

Established links between associativity equations and coordinate nets.

Identified the class of semi-Hamiltonian hydrodynamic systems related to these structures.

Provided a unified framework for understanding these interconnected systems.

Abstract

This paper is devoted to description of the relationship among oriented associativity equations, symmetry consistent conjugate curvilinear coordinate nets, and the widest associated class of semi- Hamiltonian hydrodynamic-type systems.