Abstract
We consider the continuous version of the nonlinear Hirota oscillator equation and by using the Jacobi last multiplier (JLM) show that two types of Lagrangians (or Hamiltonians) can be derived corresponding to different choices of the JLM. The existence of a mirror partner (or sister) equation is shown. Both equations belong to the Liénard-II class and the Hirota oscillator equations are shown to emerge from the requirement of isochronicity.
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Acknowledgements
Work by the author PG was supported by the Khalifa University of Science and Technology under Grant Number FSU-2021-014. He is also extremely grateful to Professor Jaume Llibre for valuable suggestions. Finally we would like to thank the two anonymous reviewers for their suggestions and valuable comments.
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Ghose-Choudhury, A., Guha, P. Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations. Qual. Theory Dyn. Syst. 21, 144 (2022). https://doi.org/10.1007/s12346-022-00676-w
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DOI: https://doi.org/10.1007/s12346-022-00676-w