• Painlevé analysis and integrability of the damped anharmonic oscillator equation

• # Fulltext

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&gt;0,B arbitrary, (ii)d2=9A/2,B=0,A&gt;0,C arbitrary and (iii)d2=−9A/4,C=2B2/(9A),A&lt;0,C&lt;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

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

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019