Euler Equations of the Generalized Bott-Virasoro Group

TL;DR

This paper generalizes the Bott-Virasoro group using connection cochains, derives new Euler equations, and explores their relationships and applications to geodesic and Burgers equations.

Contribution

It introduces a generalized Bott-Virasoro group framework and derives associated Euler equations, expanding understanding of their geometric and analytical properties.

Findings

Derived new Euler equations for the generalized Bott-Virasoro group

Established relationships between new and classical Euler equations

Analyzed geodesic equations related to Burgers equation

Abstract

In this paper, we will generalize the Bott-Virasoro group, applying the concept of the connection cochain, and derive the Euler equations corresponding to the generalized Bott-Virasoro group. We will show the relationships between the new Euler equations and the old ones. Moreover, we will study the geodesic equation corresponding to the Burgers equation and apply it to the exponential curve.