On perturbations of a class of systems of differential equations containing resonances. (Q1432168)

Consider the perturbed system \((*) \;dy_k / dt - i\lambda_k y_k + \sum_q \varepsilon^q P_{q,k} \), \(k = 1, \dots ,n,\) where \(P_{q,k}\) is a finite sum of functions \(\psi_m = y_1^{m_1} y^{m2}_2 \dots y^{m_n}_n\). The authors describes an algorithmic approach to find an approximate solution of \((*)\) which is based on an algebraic method (cf. the monograph [Algebraic methods in nonlinear perturbation theory. Moskva: Nauka (1987; Zbl 0611.34002)].