Nonlocal Transformations of Force-Free Duffing-van der Pol equation

Abstract

In this study, the nonlocal transformation methods applied to the nonlinear differential equations and the first integrals obtained by using these transformations are examined. It is shown that the linearized equations by these nonlocal transformations can be integrated by the first integrals. Then, the force-free Duffing-van der Pol oscillator equation is considered, and it is demonstrated this equation with a specific nonlinear term is integrable. To do them, first, this equation is classified by using special functions. Then, an effective procedure is emphasized to obtain a nonlocal transformation pair called Sundman. The Sundman transformation pair is found by concerning this classification. The first integrals of this equation are acquired by this Sundman transformation pair.