Invariant solutions of the supersymmetric version of a two-phase fluid flow system

TL;DR

This paper develops a supersymmetric extension of a two-phase fluid flow system, analyzes its symmetries, classifies subalgebras, and derives general solutions using symmetry reduction, involving both fermionic and bosonic variables.

Contribution

It introduces a supersymmetric version of the two-phase fluid flow system, computes its Lie superalgebra, classifies subalgebras, and finds general solutions with symmetry methods.

Findings

Lie superalgebra of the supersymmetric system is computed.

Classification of 63 subalgebras into conjugation classes is performed.

General solutions are expressed in terms of arbitrary functions of fermionic and bosonic variables.

Abstract

A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this superalgebra into 63 equivalence conjugation classes is performed. For some of the subalgebras, it is found that the invariants have a non-standard structure. For six selected subalgebras, the symmetry reduction method is used to find invariants, orbits of the subgroups and reduced systems. Through the solutions of the reduced systems, the most general solutions are expressed in terms of arbitrary functions of one or two fermionic and one bosonic variables.