On the reduction of nonlinear oscillator-equations to Abel forms (Q1881697)

The author considers the existence of analytical solutions for the nonlinear ordinary differential equations governing the Duffing, Rayleigh and Van der Pol oscillators. These equations represent a subset of a larger class of particular ordinary differential equations in mathematical physics, governing problems with strong nonlinearities. There are made several efforts to obtain solutions for the nonlinear ordinary differential equations considered in this paper. However, exact analytical solutions in terms of known functions are still lacking. Here, the author using a series of functional transformations, finally reduces all equations considered in the paper to Abel's equations of second kind that do not have exact analytical solutions.