Dispersionless Pfaff-Toda hierarchy and elliptic L\"owner equation

TL;DR

This paper links the dispersionless Pfaff-Toda hierarchy to elliptic L"owner equations, revealing a new integrable structure through one-variable reductions.

Contribution

It introduces a novel connection between the dispersionless Pfaff-Toda hierarchy and elliptic L"owner equations, expanding understanding of integrable systems.

Findings

Reduction of the hierarchy is described by coupled elliptic L"owner equations.

Establishes a new integrable structure in dispersionless limits.

Provides a framework for analyzing similar hierarchies.

Abstract

We show that one-variable reductions of the Pfaff-Toda integrable hierarchy in the dispersionless limit are described by a system of coupled elliptic L\"owner (Komatu-Goluzin) equations.