Additional symmetry of the modified extended Toda hierarchy

TL;DR

This paper introduces a new integrable hierarchy called the modified extended Toda hierarchy, incorporating additional symmetries and structures, and demonstrating its bi-Hamiltonian and tau symmetry properties.

Contribution

It constructs the METH using logarithmic Lax operators and reveals its additional symmetry flows form an infinite-dimensional Lie algebra of Block type.

Findings

METH is a new integrable hierarchy with complete flows.

The hierarchy exhibits bi-Hamiltonian structure and tau symmetry.

Additional symmetry flows form an infinite-dimensional Lie algebra of Block type.

Abstract

In this paper, one new integrable modified extended Toda hierarchy(METH) is constructed with the help of two logarithmic Lax operators. With this modification, the interpolated spatial flow is added to make all flows complete. To show more integrable properties of the METH, the bi-Hamiltonian structure and tau symmetry of the METH will be given. The additional symmetry flows of this new hierarchy are presented. These flows form an infinite dimensional Lie algebra of Block type.