Invariant solutions of the supersymmetric sinh-Gordon equation

TL;DR

This paper conducts a systematic symmetry analysis of the supersymmetric sinh-Gordon equation, deriving invariant solutions and comparing them with related equations, highlighting nonstandard invariants.

Contribution

It extends the symmetry reduction method to the supersymmetric sinh-Gordon equation and discusses nonstandard invariants, providing new insights into its solution structure.

Findings

Derived the Lie superalgebra of symmetries.

Obtained invariant solutions via symmetry reduction.

Compared results with supersymmetric sine-Gordon equation.

Abstract

A systematic group-theoretical analysis of the supersymmetric sinh-Gordon equation is performed. A generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and the method of symmetry reduction is applied in order to obtain invariant solutions of the supersymmetric sinh-Gordon equation. The results are compared with those previously found for the supersymmetric sine-Gordon equation. The presence of nonstandard invariants is discussed for the supersymmetric sinh-Gordon equation, as well as for the supersymmetric Korteweg-de Vries equation.