Periodic solutions of strongly quadratic non-linear oscillators by the elliptic Lindstedt-Poincaré method

The elliptic Lindstedt-Poincaré method is used/employed to study the periodic solutions of quadratic strongly non-linear oscillators of the form ẍ + c1x + c2x2 = ε f(x,. ẋ), in which the Jacobian elliptic functions are employed instead of the usual circular functions in the classical Lindstedt-Poincaré method. The generalized Van de Pol equation with f(x, ẋ) = μ0 + μ1x - μ2x2 is studied in detail. Comparisons are made with the solutions obtained by using the Lindstedt-Poincaré method and Runge-Kutta method to show the efficiency of the present method. © 1999 Academic Press.link_to_subscribed_fulltex