Is it possible to use the multiple scales technique to a set of coupled ODEs?

Question

I need to solve a set of coupled ODEs. The ODEs are well indicated for using the multiple scales method (generalised oscillator equations), I have just never done such a thing on a ODEs set. Is it possible? How should I adapt the steps?

Please note: Since there is a good chance I haven't been lucky enough finding in literature and google, I'll be really glad for an online reference as well.

EDIT: Please, provide minimal working example or a reference containing it.

Answer 1

I would recommend

F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, 2006, ISBN 978-3-540-60934-6;

starting with chapter 9, several methods of multiple scale analysis are treated, with extensive use of examples. For another slightly more general reference, see

C. Kuehn, Multiple Time Scale Dynamics, Springer, 2015, ISBN 978-3-319-12316-5.

Without more specific information on your system, it's difficult to give a suitable working example.

Some online resources can be found here, here, here, or here. I recommend you use a book, though.