A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation

TL;DR

This paper develops a vertex operator framework for solutions to the Gurevich-Zybin hydrodynamical hierarchy, utilizing spectral and Lie algebraic methods to generate an infinite hierarchy of integrable flows.

Contribution

It introduces a novel vertex operator representation for the Gurevich-Zybin hierarchy using spectral and Lie algebraic techniques.

Findings

Constructed vertex operator representation for solutions.

Generated an infinite hierarchy of dispersive Lax type flows.

Provided a functional representation for the hierarchy.

Abstract

An approach based on the spectral and Lie - algebraic techniques for constructing vertex operator representation for solutions to a Riemann type Gurevicz-Zybin hydrodynamical hierarchy is devised. A functional representation generating an infinite hirerachy of dispersive Lax type integrable flows is obtaned.