WKB approach applied to 1D time-dependent nonlinear Hamiltonian oscillators

Marko Robnik

University of Maribor, Slovenia

We present a simple WKB-like approach to obtain approximate analytic solutions to a certain class of time-dependent nonlinear 1D Hamiltonian oscillators. The case of homogeneous power law potentials is solved explicitly in closed form in the leading order. The accuracy of the approximation is surprisingly good and we illustrate it in case of the quartic oscillator. The method is expected to be useful in treating the statistical properties of the dynamical quantities (like energy and adiabatic invariant) in nonlinear oscillators, and in many other applications in nonlinear oscillators.