Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations
Joint Authors
Davachi, N.
Rosario-Franco, M.
Musielak, Zdzislaw E.
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-06-22
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations.
The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup.
For the null Lagrangians, their corresponding gauge functions are derived.
The obtained Lagrangians are either new or generalization of those previously known.
The previously developed Lie group approach to derive some equations of the semigroup is also described.
It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined.
A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.
American Psychological Association (APA)
Musielak, Zdzislaw E.& Davachi, N.& Rosario-Franco, M.. 2020. Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1174507
Modern Language Association (MLA)
Musielak, Zdzislaw E.…[et al.]. Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations. Journal of Applied Mathematics No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1174507
American Medical Association (AMA)
Musielak, Zdzislaw E.& Davachi, N.& Rosario-Franco, M.. Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1174507
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174507