Generalized Miura Transformations, Two-Boson KP Hierarchies and their Reduction to KDV Hierarchies

TL;DR

This paper explores gauge equivalences between two-boson KP hierarchies and their reductions to KdV hierarchies, establishing generalized Miura transformations linking these integrable systems.

Contribution

It introduces a framework for gauge equivalence between two-boson KP hierarchies and their reduction to classical KdV hierarchies via symplectic reduction.

Findings

Gauge equivalence between two-boson KP hierarchies established

Reduction to KdV, mKdV, Schwarzian KdV hierarchies demonstrated

Miura maps derived as gauge transformations

Abstract

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV, mKdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies.