A two-component generalization of Burgers equation with Quasi-periodic solutions

TL;DR

This paper develops a theta function framework for quasi-periodic solutions of a two-component Burgers equation, utilizing algebraic curve theory and Baker-Akhiezer functions to derive explicit representations.

Contribution

It introduces a novel two-component generalization of Burgers equation and provides explicit quasi-periodic solutions using advanced algebraic geometry tools.

Findings

Explicit theta function representations derived

Solutions characterized by algebraic curve theory

Method applicable to other integrable systems

Abstract

In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers equation. Our tools include the theory of algebraic curve, the meromorphic function, Baker-Akhiezer functions, the Dubrovin-type equations for auxiliary divisor, with these tools, the explicit representa- tions for above quantities are obtained.