Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability
المؤلفون المشاركون
Ayub, Muhammad
Khan, Masood
Mahomed, Fazal Mahmood
المصدر
Journal of Applied Mathematics
العدد
المجلد 2013، العدد 2013 (31 ديسمبر/كانون الأول 2013)، ص ص. 1-15، 15ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2013-04-03
دولة النشر
مصر
عدد الصفحات
15
التخصصات الرئيسية
الملخص EN
We present a systematic procedure for the determination of a complete set of kth-order (k≥2) differential invariants corresponding to vector fields in three variables for three-dimensional Lie algebras.
In addition, we give a procedure for the construction of a system of two kth-order ODEs admitting three-dimensional Lie algebras from the associated complete set of invariants and show that there are 29 classes for the case of k = 2 and 31 classes for the case of k≥3.
We discuss the singular invariant representations of canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras.
Furthermore, we give an integration procedure for canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras which comprises of two approaches, namely, division into four types I, II, III, and IV and that of integrability of the invariant representations.
We prove that if a system of two second-order ODEs has a three-dimensional solvable Lie algebra, then, its general solution can be obtained from a partially linear, partially coupled or reduced invariantly represented system of equations.
A natural extension of this result is provided for a system of two kth-order (k≥3) ODEs.
We present illustrative examples of familiar integrable physical systems which admit three-dimensional Lie algebras such as the classical Kepler problem and the generalized Ermakov systems that give rise to closed trajectories.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Ayub, Muhammad& Khan, Masood& Mahomed, Fazal Mahmood. 2013. Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-449554
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Ayub, Muhammad…[et al.]. Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability. Journal of Applied Mathematics No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-449554
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Ayub, Muhammad& Khan, Masood& Mahomed, Fazal Mahmood. Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-449554
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-449554
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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