• PT-symmetric dimer of coupled nonlinear oscillators

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      https://www.ias.ac.in/article/fulltext/pram/085/05/0915-0928

    • Keywords

       

      PT -symmetry; dimer; rotating wave approximation; novel superposition.

    • Abstract

       

      We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.

    • Author Affiliations

       

      Avinash Khare1 2

      1. Indian Institute of Science Education and Research (IISER), Homi Bhabha Road, Pashan, Pune 411 008, India
      2. Physics Department, Savitribai Phule Pune University, Pune 411 007, India
    • Dates

       
  • Pramana – Journal of Physics | News

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