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Approximate Mei Symmetries and Invariants of the Hamiltonian

Author

Listed:
  • Umara Kausar

    (School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan
    These authors contributed equally to this work.)

  • Tooba Feroze

    (School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan
    These authors contributed equally to this work.)

Abstract

It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of finding approximate Mei symmetries and invariants of the perturbed/approximate Hamiltonian is presented that can be used in different fields of study where approximate Hamiltonians are under consideration. The results are presented in the form of theorems along with their proofs. A simple example of mechanics is considered to elaborate the method of finding these symmetries and the related Mei invariants. At the end, a comparison of approximate Mei symmetries and approximate Noether symmetries is also given. The comparison shows that there is only one common symmetry in both sets of symmetries. Hence, rest of the symmetries in the two sets correspond to two different sets of conserved quantities.

Suggested Citation

  • Umara Kausar & Tooba Feroze, 2021. "Approximate Mei Symmetries and Invariants of the Hamiltonian," Mathematics, MDPI, vol. 9(22), pages 1-8, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2910-:d:679788
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    References listed on IDEAS

    as
    1. Yu-Shan Bai & Qi Zhang, 2018. "Approximate Symmetry Analysis and Approximate Conservation Laws of Perturbed KdV Equation," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-11, September.
    2. Xiang-Hua Zhai & Yi Zhang, 2020. "Mei Symmetry and New Conserved Quantities of Time-Scale Birkhoff’s Equations," Complexity, Hindawi, vol. 2020, pages 1-7, January.
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