A general solution procedure for coupled systems with arbitrary internal resonances
The author deals with equations of motion where the linear parts are uncoupled, while quadratic and cubic nonlinearities are expressed by arbitrary spatial differential (or integral) operators. An external excitation acts on the first equation only. Using the method of multiple scales, the author obtains a general approximate solution, and then derives amplitude and phase equations. The results are applied to a simple case of two coupled equations.
scientific article; zbMATH DE number 1741893