# Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model

## TL;DR

This paper thoroughly analyzes the symmetries, conservation laws, and Hamiltonian structures of an isothermal no-slip drift flux model, revealing its integrability properties and algebraic structures.

## Contribution

It provides a complete classification of symmetries, conservation laws, and Hamiltonian structures for the model, including new recursion operators and infinite Hamiltonian families.

## Key findings

- Exhaustive description of generalized symmetries and conservation laws.
- Identification of a generating set of conservation laws with two zeroth-order laws.
- Construction of infinite Hamiltonian structures and associated symmetry algebras.

## Abstract

We study the hydrodynamic-type system of differential equations modeling isothermal no-slip drift flux. Using the facts that the system is partially coupled and its subsystem reduces to the (1+1)-dimensional Klein--Gordon equation, we exhaustively describe generalized symmetries, cosymmetries and local conservation laws of this system. A generating set of local conservation laws under the action of generalized symmetries is proved to consist of two zeroth-order conservation laws. The subspace of translation-invariant conservation laws is singled out from the entire space of local conservation laws. We also find broad families of local recursion operators and a nonlocal recursion operator, and construct an infinite family of Hamiltonian structures involving an arbitrary function of a single argument. For each of the constructed Hamiltonian operators, we obtain the associated algebra of Hamiltonian symmetries.