# Extended symmetry analysis of isothermal no-slip drift flux model

## TL;DR

This paper conducts an extensive symmetry analysis of an isothermal no-slip drift flux model, revealing its infinite-dimensional Lie algebra, symmetries, and solutions, including linearizations and conservation laws.

## Contribution

It provides a comprehensive symmetry classification, including the complete point symmetry group and generalized symmetries, for the drift flux system and its subsystem.

## Key findings

- Infinite-dimensional Lie invariance algebra identified.
- Complete point symmetry group including discrete symmetries found.
- General solutions constructed via linearization and hodograph methods.

## Abstract

We perform extended group analysis for a system of differential equations modeling an isothermal no-slip drift flux. The maximal Lie invariance algebra of this system is proved to be infinite-dimensional. We also find the complete point symmetry group of this system, including discrete symmetries, using the megaideal-based version of the algebraic method. Optimal lists of one- and two-dimensional subalgebras of the maximal Lie invariance algebra in question are constructed and employed for obtaining reductions of the system under study. Since this system contains a subsystem of two equations that involves only two of three dependent variables, we also perform group analysis of this subsystem. The latter can be linearized by a composition of a fiber-preserving point transformation with a two-dimensional hodograph transformation to the Klein-Gordon equation. We also employ both the linearization and the generalized hodograph method for constructing the general solution of the entire system under study. We find inter alia genuinely generalized symmetries for this system and present the connection between them and the Lie symmetries of the subsystem we mentioned earlier. Hydrodynamic conservation laws and their generalizations are also constructed.