Explicit characterization of some commuting differential operators of rank 2
Vardan Oganesyan
TL;DR
This paper characterizes specific commuting differential operators of rank 2, focusing on an operator of order 4 with potential functions, and explores their commutativity conditions and examples.
Contribution
It provides explicit conditions for the commutativity of a fourth-order differential operator with higher-order operators of rank 2, including novel examples.
Findings
Derived explicit commutativity conditions for operators of rank 2.
Constructed examples of commuting operators that do not commute with odd-order operators.
Identified structural properties of rank 2 differential operators.
Abstract
In this paper we consider differential opeartor L=d^4_x + u(x). We find the commutativity condition for operator L with a differential operator M of order 4g+2, where L and M are operators of rank 2. Some examples are constructed. These examples don't commute with differential opeartors of odd order.
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