WKB approach applied to 1D time-dependent nonlinear Hamiltonian oscillators. (English) Zbl 1337.34061
Summary: 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.
MSC:
| 34E20 | Singular perturbations, turning point theory, WKB methods for ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
