On asymptotic approximations of first integrals for a class of nonlinear oscillators

In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for the nonlinear differential equations are constructed by using the recently developed perturbation method based on integrating vectors. The existence and the stability of time-periodic solutions can be determined from these...

On approximations of first integrals for strongly nonlinear oscillators

On approximations of first integrals for a system of weakly nonlinear, coupled harmonic oscillators

In this paper a system of weakly nonlinear, coupled harmonic oscillators will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate rst integrals and periodic solutions. To show how this perturbation method works the method is applied to a system of weakly nonlinear,...