On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces

Abstract

The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of the symmetry properties of both the classical and supersymmetric versions of the Gauss-Weingarten equations is performed. A supersymmetric generalization of the conjecture establishing the necessary conditions for a system to be integrable in the sense of soliton theory is formulated and illustrated by the examples of supersymmetric versions of the sine-Gordon equation and the Gauss-Codazzi equations.

References in corpus (6)

• A supersymmetric Sawada-Kotera equation
• Classification of supersymmetries
• On Darboux transformation of the supersymmetric sine-Gordon equation
• On linearization of super sine-Gordon equation
• A Class of Soliton Solutions for the N=2 Super mKdV/Sinh-Gordon Hierarchy
• Fermionic supersymmetric extension of the Gauss-Weingarten and Gauss-Codazzi equations

Cited by in corpus (2)

• On integrability aspects of the supersymmetric sine-Gordon equation
• Supersymmetric versions of the Fokas-Gel'fand formula for immersion