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    • Painlevé analysis and integrability of the damped anharmonic oscillator equation

      S Paul Raj S Rajasekar

      Volume 45 Issue 4 October 1995 pp 305-309

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      https://www.ias.ac.in/article/fulltext/pram/045/04/0305-0309

    • Keywords

       

      Anharmonic oscillator; Painlevé analysis; exact solution

    • Abstract

       

      The Painlevé analysis is applied to the anharmonic oscillator equation$$\ddot x + d\dot x + Ax + Bx^2 + Cx^3 = 0$$. The following three integrable cases are identified: (i)C=0,d2=25A/6,A>0,B arbitrary, (ii)d2=9A/2,B=0,A>0,C arbitrary and (iii)d2=−9A/4,C=2B2/(9A),A<0,C<0,B arbitrary. The first two integrable choices are already reported in the literature. For the third integrable case the general solution is found involving elliptic function with exponential amplitude and argument.

    • Author Affiliations

       

      S Paul Raj1 S Rajasekar1 2

      1. Department of Physics, St. Xavier’s College, Tirunelveli - 627 002, India
      2. Department of Physics, Manonmaniam Sundaranar University, Tirunelveli - 627 002, India

    • Dates

       
      Published
      October 1995
      Manuscript received
      24 April 1995
      Manuscript revised
      9 August 1995

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