Asymptotic expansions of the period solutions of nonlinear evolution equations
A spectral technique for building asymptotic expansions which describe periodic processes in conservative and self-excited systems is presented. The small parameter of the expansion is connected with the ratio of the amplitudes of higher than the first harmonics. In the case of an oscillator with power nonlinearity the frequency of the main harmonic and the complex amplitudes of higher harmonics are computed. In the simplest case of weakly nonlinear oscillations the complete asymptotic expansion is shown to be valid in the whole domain of the periodic motions of definite type until the separatrix is reached. For some special cases of strongly nonlinear oscillations the comparison of the results with known exact solutions is carried out and criteria of convergence of the expansions are determined.
scientific article; zbMATH DE number 1185503