A theory of exactly integrable quadratic Liénard type equations. (English) Zbl 1372.34001

Summary: The dynamics of quadratic Liénard type equations is usually investigated in the only context of periodic solutions. The problem of interest in this work is then to demonstrate the existence of a simple variable transformation generating a class of exactly integrable quadratic Liénard type equations that preserves the three distinct damped dynamical operating regimes of nonlinear oscillators. Specific examples of equation belonging to this class and their exact solutions in terms of the periodic solution to linear harmonic oscillator are provided for illustrating the developed theory.


34A05 Explicit solutions, first integrals of ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34A34 Nonlinear ordinary differential equations and systems
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