2004/04/01 by V. K. Chandrasekar, V K Chandrasekar, M. Senthilvelan +3 · 1 citation
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical methods for differential equations #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/0305-4470/37/16/004
published as J. Phys. A: Math. Gen. 37 (2004) 4527-4534 · 8 pages, 1 figure, J. Phys. A: Math. Gen. 37 (2004) to appear
arxiv created 2004/04/01 · openalex publication_date 2004/04/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
In this paper, we show that the force-free Duffing–van der Pol oscillator is completely integrable for a specific parametric choice. We derive a general solution for this parametric choice. Further, we describe a procedure to construct the transformation which removes the time-dependent part from the first integral and provide the general solution by quadrature. The procedure is shown to have a wider applicability through additional examples. We also show that through our method one can deduce linearizing transformations in a simple and straightforward way and illustrate it with a specific example.