Integrals of open 2D lattices

TL;DR

This paper derives explicit formulas for integrals of open 2D Toda lattices of type A_n, demonstrating their application to various reductions and establishing connections with other lattice systems.

Contribution

It provides a new explicit formula for integrals of open 2D Toda lattices and explores their relations to other lattice types like G_2 and Shabat-Yamilov lattices.

Findings

Explicit integral formulas for open 2D Toda lattices of type A_n

Application of formulas to Toda G_2 lattice

Connection established between open Toda A_n and Shabat-Yamilov lattices

Abstract

We present an explicit formula for integrals of the open 2D Toda lattice of type $A_n$. This formula is applicable for various reductions of this lattice. To illustrate the concept we find integrals of the Toda $G_2$ lattice. We also reveal a connection between the open Toda $A_n$ and Shabat-Yamilov lattices.