Integrability of Exceptional Hydrodynamic Type Systems

TL;DR

This paper investigates the integrability of non-diagonalisable hydrodynamic systems, specifically those related to the Mikhalev equation, and demonstrates their reducibility to the Heat hierarchy, providing new explicit solutions.

Contribution

It introduces a method to analyze non-diagonalisable hydrodynamic systems and connects them to the Heat hierarchy, offering new explicit solutions for the Mikhalev equation.

Findings

Families of hydrodynamic systems are reducible to the Heat hierarchy.

New explicit solutions for the Mikhalev equation are constructed.

The study extends integrability analysis to non-diagonalisable systems.

Abstract

In this paper we consider non-diagonalisable hydrodynamic type systems integrable by the Extended Hodograph Method. We restrict our consideration to non-diagonalisable hydrodynamic reductions of the Mikhalev equation. We show that families of these hydrodynamic type systems are reducible to the Heat hierarchy. Then we construct new particular explicit solutions for the Mikhalev equation.