Multi-component Pfaff-Toda hierarchy within bilinear formalism

TL;DR

This paper introduces the multi-component Pfaff-Toda hierarchy using free fermions and bosonization, deriving bilinear equations and functional relations for its tau-function within a bilinear formalism.

Contribution

It presents a novel multi-component Pfaff-Toda hierarchy framework and derives its fundamental bilinear equations using free fermion and bosonization techniques.

Findings

Derived a generating bilinear integral equation for the tau-function.

Obtained bilinear functional relations of Hirota-Miwa type.

Established a new hierarchy within the bilinear formalism.

Abstract

Using the free fermions technique and non-abelian bosonization rules we introduce the multi-component Pfaff-Toda hierarchy. The tau-function is defined as vacuum expectation value of a Clifford group element of the algebra of Fermi-operators. A generating bilinear integral equation for the tau-function is obtained. A number of bilinear functional relations for the tau-function of the Hirota-Miwa type are derived as corollaries of the generating bilinear equation.