Commutativity and Commutative Pairs of Some Differential Equations

Köksal M. E.

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, cilt.9, sa.4, ss.689-703, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.26713/cma.v9i4.901
  • Dergi Adı: COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.689-703
  • Anahtar Kelimeler: Commutativity, Differential equations, Analytic solutions, Analogue control, Robust control, Cryptology
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.