An Operator Approach to the Integration of Linear Differential Equations

arXiv (Cornell University) 2026 Preprint Open access

Read full text
Authors: Oleg Viktorovich Kaptsov
DOI: 10.48550/arxiv.2602.13674
Cited by: 0

Abstract

We develop an operator approach to the integration of linear differential equations based on intertwining relations between differential operators. Conditions for the existence of intertwining operators are obtained, and it is shown that, in low-order cases, the problem reduces to Riccati-type equations. The method is applied to linear partial differential equations, which makes it possible to construct their solutions. The linear Klein--Gordon equation is presented as an illustrative example.

Fields of Study & Subjects

Differential Equations and Boundary Problems Nonlinear Waves and Solitons Spectral Theory in Mathematical Physics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
14 February 2026
Language
EN
Document type
Preprint