Solution of the dispersionless Hirota equations

TL;DR

This paper demonstrates that the dispersionless differential Fay identity can be used to algebraically characterize and solve the dispersionless Hirota equations, offering a universal approach.

Contribution

It establishes an algebraic framework linking the differential Fay identity to the dispersionless Hirota equations, including kernel expansion and D-bar data analysis.

Findings

Kernel expansion provides a universal algebraic solution.

Differential Fay identity is equivalent to the kernel characterization.

D-bar data analysis offers additional insights.

Abstract

The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.