Application of the Jacobi method and integrating factors to a class of Painleve-Gambier equations

YAŞAR, EMRULLAH; REİS, MURAT

doi:10.1088/1751-8113/43/29/295202

Application of the Jacobi method and integrating factors to a class of Painleve-Gambier equations

Atıf İçin Kopyala

YAŞAR E., REİS M.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.43, sa.29, 2010 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 43 Sayı: 29
Basım Tarihi: 2010
Doi Numarası: 10.1088/1751-8113/43/29/295202
Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this work, we consider the motion of chain ball drawing with constant force in the frictionless surface which is a class of the Painleve-Gambier equations. We apply Jacobi's method which enables us to obtain Lagrangians of any second-order differential equation. It is comprised that the Lagrangian obtained by Musielak's method is the particular case of the many Lagrangians that can be obtained by Jacobi's method. In addition, we obtain integrating factors and first integrals for the equation in question by Ibragimov's variational derivative approach.