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Pramana

, Volume 62, Issue 1, pp 1–12 | Cite as

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

  • S. Rajasekar
Article

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.

Keywords

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

PACS Nos

02.30.Ik 02.30.Hq 02.30.Gp 05.45.Xt 

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Copyright information

© Indian Academy of Sciences 2004

Authors and Affiliations

  • S. Rajasekar
    • 1
  1. 1.Department of PhysicsManonmaniam Sundaranar UniversityTirunelveliIndia

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