Supersymmetric formulation of the minimal surface equation: algebraic aspects

TL;DR

This paper develops a supersymmetric extension of the minimal surface equation, analyzes its symmetry properties, classifies subalgebras, and derives invariant solutions, providing a deeper algebraic understanding of the equation.

Contribution

It introduces a supersymmetric formulation of the minimal surface equation and classifies its symmetry subalgebras, which is a novel algebraic approach.

Findings

Identified a Lie superalgebra of symmetries for the supersymmetric equation.

Classified 143 conjugacy classes of one-dimensional subalgebras.

Derived invariant solutions using symmetry reduction.

Abstract

In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version.