Commutativity and Commutative Pairs of Some Differential Equations

Authors

  • Mehmet Emir Koksal Department of Mathematics, Ondokuz Mayis University, 55139 Atakum, Samsun

DOI:

https://doi.org/10.26713/cma.v9i4.901

Keywords:

Commutativity, differential equations, analytic solutions, analogue control, robust control, cryptology

Abstract

In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order linear differential equations with variable coefficients. It is shown that the system modeled by each one of these equations has a commutative pair with(or without) some conditions or not. There appear special cases such that both, only one or neither of the original system and its commutative pair has explicit analytic solution. Some benefits of commutativity have already been mentioned in the literature but a new application in cryptology for obscuring transmitted signals in telecommunication is illustrated in this paper.

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Published

28-12-2018
CITATION

How to Cite

Koksal, M. E. (2018). Commutativity and Commutative Pairs of Some Differential Equations. Communications in Mathematics and Applications, 9(4), 689–703. https://doi.org/10.26713/cma.v9i4.901

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

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