Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

TL;DR

This paper develops a supersymmetric extension of a hydrodynamic system using superfield formalism, analyzes its symmetries, and constructs various invariant solutions including waves and exponential forms.

Contribution

It introduces a novel supersymmetric formulation of hydrodynamic equations and classifies their symmetries to find explicit invariant solutions.

Findings

Supersymmetric hydrodynamic model formulated in superspace.

Lie superalgebras of classical and supersymmetric models computed.

Multiple classes of invariant solutions constructed, including waves and exponential solutions.

Abstract

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.