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

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 a closed form in the leading order. The accuracy of the approximation is surprisingly good and we illustrate it in the case of the quartic oscillator.