• Painlevé analysis and integrability of two-coupled non-linear oscillators

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      https://www.ias.ac.in/article/fulltext/pram/062/01/0001-0012

    • Keywords

       

      Two-coupled non-linear oscillators; Painlevé analysis; exact analytical solution

    • Abstract

       

      Integrability of a linearly damped two-coupled non-linear oscillators equation$$\begin{gathered} \mathop x\limits^{..} = - d\mathop {\mathop x\limits^. - \alpha x - \delta _1 (x^2 + y^2 ) - 2\delta _2 xy}\limits^. \hfill \\ \mathop y\limits^{..} = d\mathop y\limits^. - \beta y - \delta _2 (x^2 + y^2 ) - 2\delta _1 xy \hfill \\ \end{gathered} $$ is investigated by employing the Painlevé analysis. The following two integrable cases are identified: (i)d = 0, α =β, δ_1 and δ_2 are arbitrary, (ii) d^2= 25α/6, α =β, δ_1 and δ_2 are arbitrary. Exact analytical solution is constructed for the integrable choices.

    • Author Affiliations

       

      S Rajasekar1

      1. Department of Physics, Manonmaniam Sundaranar University, Tirunelveli - 627 012, India
    • Dates

       
  • Pramana – Journal of Physics | News

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