On the Classical $W_{4}^{(2)}$ Algebra

TL;DR

This paper explores the classical W_{4}^{(2)} algebra by constructing associated integrable equations, presenting Miura maps and free field realizations, and developing Toda type integrable systems for it.

Contribution

It introduces new integrable systems and free field realizations for the classical W_{4}^{(2)} algebra, expanding understanding of its structure and applications.

Findings

Constructed integrable evolution equations for W_{4}^{(2)}.

Presented Miura maps and their modifications.

Developed Toda type integrable systems related to the algebra.

Abstract

We consider the classical \w42 algebra from the integrable system viewpoint. The integrable evolution equations associated with the \w42 algebra are constructed and the Miura maps , consequently modifications, are presented. Modifying the Miura maps, we give a free field realization the classical \w42 algebra. We also construct the Toda type integrable systems for it.