Supersymmetric version of a Gaussian irrotational compressible fluid flow

TL;DR

This paper extends a Gaussian irrotational compressible fluid flow model to include supersymmetry, deriving new invariant solutions and classifying its symmetry algebra.

Contribution

It introduces a supersymmetric extension of the fluid flow model and systematically derives invariant solutions using symmetry reduction.

Findings

New algebraic solutions including solitons and periodic waves

Classification of the supersymmetry algebra and subalgebras

Explicit forms of hyperbolic and multi-solitonic solutions

Abstract

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield formalism. The Lie superalgebra of this extended model is determined and a classification of its subalgebras is performed. The method of symmetry reduction is systematically applied in order to derive special classes of invariant solutions of the supersymmetric model. Several new types of algebraic, hyperbolic, multi-solitonic and doubly periodic solutions are obtained in explicit form.