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.
Volume 94, 2020
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