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      https://www.ias.ac.in/article/fulltext/pram/085/05/0755-0787

    • Keywords

       

      Lie point symmetries; 𝜆-symmetries; Noether symmetries; contact symmetries; adjoint symmetries; nonlocal symmetries; hidden symmetries; telescopic vector fields.

    • Abstract

       

      Lie symmetry analysis is one of the powerful tools to analyse nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries, hidden symmetries, nonlocal symmetries, 𝜆-symmetries, adjoint symmetries and telescopic vector fields of a secondorder ordinary differential equation. We also illustrate the algorithm involved in each method by considering a nonlinear oscillator equation as an example. The connections between

      1. symmetries and integrating factors and

      2. symmetries and integrals are also discussed and illustrated through the same example.

      The interconnections between some of the above symmetries, i.e.,

      1. Lie point symmetries and 𝜆-symmetries and

      2. exponential nonlocal symmetries and 𝜆-symmetries are also discussed.

      The order reduction procedure is invoked to derive the general solution of the second-order equation.

    • Author Affiliations

       

      M Senthilvelan1 V K Chandrasekar2 R Mohanasubha1

      1. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
      2. Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401, India
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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