• S Paul Raj

Articles written in Pramana – Journal of Physics

• Painlevé analysis and integrability of the damped anharmonic oscillator equation

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.

• The Painlevé property, integrability and chaotic behaviour of a two-coupled Duffing oscillators

Integrability and chaotic behaviour in a two-coupled Duffing oscillators are studied. The coupling is nonlinear. Painlevé test is performed to identify integrable cases of damped- and force-free system. Exact analytical solutions are given for the integrable cases. Effect of external periodic forces for (i) single well with infinite height potential, (ii) potential with a hump at the centre and (iii) single well with finite height hump potential are numerically investigated. Occurrence of multiple attractors and period doubling cascades of coexisting attractors is presented.

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019