Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians
Non-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Fir...
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| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/8/1061 |
| _version_ | 1811300307852853248 |
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| author | Yi Zhang Xue-Ping Wang |
| author_facet | Yi Zhang Xue-Ping Wang |
| author_sort | Yi Zhang |
| collection | DOAJ |
| description | Non-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Firstly, the definition, criterion, and corresponding new conserved quantity of Mei symmetry in this system are presented and studied. Secondly, considering that a small disturbance is applied on the system, the differential equations of the disturbed motion are established, the definition of Mei symmetry and corresponding criterion are given, and the new adiabatic invariants led by Mei symmetry are proposed and proved. Examples also show the validity of the results. |
| first_indexed | 2024-04-13T06:49:09Z |
| format | Article |
| id | doaj.art-2558fd87971547b3bce272ca03ed7eee |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T06:49:09Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2558fd87971547b3bce272ca03ed7eee2022-12-22T02:57:28ZengMDPI AGSymmetry2073-89942019-08-01118106110.3390/sym11081061sym11081061Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard LagrangiansYi Zhang0Xue-Ping Wang1College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, ChinaCollege of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, ChinaNon-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Firstly, the definition, criterion, and corresponding new conserved quantity of Mei symmetry in this system are presented and studied. Secondly, considering that a small disturbance is applied on the system, the differential equations of the disturbed motion are established, the definition of Mei symmetry and corresponding criterion are given, and the new adiabatic invariants led by Mei symmetry are proposed and proved. Examples also show the validity of the results.https://www.mdpi.com/2073-8994/11/8/1061Mei symmetryconserved quantityadiabatic invariantquasi-fractional dynamical systemnon-standard Lagrangians |
| spellingShingle | Yi Zhang Xue-Ping Wang Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians Symmetry Mei symmetry conserved quantity adiabatic invariant quasi-fractional dynamical system non-standard Lagrangians |
| title | Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians |
| title_full | Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians |
| title_fullStr | Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians |
| title_full_unstemmed | Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians |
| title_short | Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians |
| title_sort | mei symmetry and invariants of quasi fractional dynamical systems with non standard lagrangians |
| topic | Mei symmetry conserved quantity adiabatic invariant quasi-fractional dynamical system non-standard Lagrangians |
| url | https://www.mdpi.com/2073-8994/11/8/1061 |
| work_keys_str_mv | AT yizhang meisymmetryandinvariantsofquasifractionaldynamicalsystemswithnonstandardlagrangians AT xuepingwang meisymmetryandinvariantsofquasifractionaldynamicalsystemswithnonstandardlagrangians |