Perturbation method, Padé approximants and exact solutions of nonlinear mechanics equationsr pages 181-189


In this article we are suggesting a method for finding exact solutions to integrable and non-integrable nonlinear mechanics equations that is based on the perturbation method. The criterion of equality of sequential diagonal Padé approximants whose minimum order is determined by the pole order of the equation’s solution is used for summation of the perturbation series. When the criterion is satisfied, the Padé approximants are the sought exact solutions.