Programming and Computer Software

, Volume 36, Issue 2, pp 97–102

# Ideals of differential operators and transformations of linear partial differential equations

• O. V. Kaptsov
Article

## Abstract

A ring of linear differential operators with smooth coefficients generated by two differentiations is considered. Concepts of operators closed with respect to commutation, a resultant of two operators, and a two-dimensional analogue of Wronskian are introduced. Sufficient conditions that two differential operators are generators of a left ideal annihilating a finite-dimensional space of functions are found. Differential operators annihilating given functions are constructed. The operators obtained transform solutions of one secondorder differential equation into solutions of another equation of the same order.

## Keywords

Left Ideal Domain Versus Darboux Transformation Order Operator Finite Dimensional Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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