Noether theory for Birkhoffian systems with nabla derivatives
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Authors
Chuanjing Song
- College of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China.
Yi Zhang
- College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, P. R. China.
Abstract
There are discrete phenomena which happen only on discrete time or hold discrete space structures such as economy series,
population dynamics et al.. Then there is a tool needed for these discrete issues or applications. Time scale is one of the useful
tools to solve some discrete problems. In this paper, time scale is used to establish discrete Pfaff-Birkhoff principle and achieve
discrete Birkhoff equations, discrete Noether identity and discrete conserved quantity for the discrete Birkhoffian system. Firstly,
Birkhoff equations, Noether identity and Noether theorem with nabla derivatives on time scales are investigated by using the
isochronous variational principle. Secondly, some special cases, especially the discrete Birkhoffian system are discussed. Thirdly,
another method, i.e., the duality principle is introduced for the Birkhoffian system on time scales. And finally, an example is
given to illustrate the results and methods.
Share and Cite
ISRP Style
Chuanjing Song, Yi Zhang, Noether theory for Birkhoffian systems with nabla derivatives, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 2268--2282
AMA Style
Song Chuanjing, Zhang Yi, Noether theory for Birkhoffian systems with nabla derivatives. J. Nonlinear Sci. Appl. (2017); 10(4):2268--2282
Chicago/Turabian Style
Song, Chuanjing, Zhang, Yi. "Noether theory for Birkhoffian systems with nabla derivatives." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 2268--2282
Keywords
- Noether theorem
- Birkhoffian system
- time scale
- duality principle
- isochronous variational principle.
MSC
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