Matrix commuting differential operators of rank 2

TL;DR

This paper introduces a novel method for constructing matrix commuting differential operators of rank 2, providing explicit examples of operators with orders 2 and 2g, advancing the theory of differential operators.

Contribution

The paper presents a new effective method for constructing matrix commuting differential operators of rank 2 and vector rank (2,2), including explicit examples.

Findings

Constructed new matrix commuting differential operators of orders 2 and 2g

Developed an effective method for rank 2 operators

Expanded the class of known commuting differential operators

Abstract

In this paper we propose a very effective method for constructing matrix commuting differential operators of rank 2 and vector rank (2,2). We find new matrix commuting differential operators L, M of orders 2 and 2g respectively.