Gauge equivalence problem on differential operators under fiber-preserving transformation

Bakhshandeh, Morteza; Bakhshandeh Chamazkoti, Rohollah; Nadjafikhah, Mehdi

doi:10.22103/jmmr.2024.23080.1592

Gauge equivalence problem on differential operators under fiber-preserving transformation

Document Type : Research Paper

Authors

Morteza Bakhshandeh ¹

Rohollah Bakhshandeh Chamazkoti ²

Mehdi Nadjafikhah ³

¹ Department of Mathematics‎, ‎Karaj Branch‎, ‎Islamic Azad University‎, ‎karaj‎, ‎Iran.

² Faculty of Basic Sciences, Department of Mathematics, Babol Noshirvani University of Technology, Babol, Iran

³ School of Mathematics, Iran University of Science and Technology, Tehran, Iran

10.22103/jmmr.2024.23080.1592

Abstract

This paper focuses on investigating the equivalence problem for fifth-order differential operators (FODOs) on the line under general fiber-preserving transformations. Utilizing the Cartan method of equivalence, the study specifically addresses the gauge equivalence problem, seeking to establish the conditions for two FODOs to be related by a fiber-preserving transformation. By analyzing the properties of these operators, the research aims to identify conditions for their transformation while maintaining the fiber structure. The systematic approach of the Cartan method is employed to derive the necessary conditions for gauge equivalence between these FODOs. The study aims to enhance understanding of the equivalence problem for FODOs and shed light on fiber-preserving transformations that uphold gauge equivalence.

Keywords

Differential operators

Gauge equivalence

Absorption

Normalization

Subjects

Geometry and Topology

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