Application of method of special series with functional arbitrariness in construction of solutions of nonlinear partial differential equations

In the paper an analytical method for constructing solutions of nonlinear partial differential equations based on the method of special series is considered. The essence of this approach is in representation of solutions of an original equation in the form of series with recurrently coefficients computed in powers of specially selected functions. Such functions may depend on several independent variables, and also contain arbitrary functions that may depend on a smaller number of independent variables. The paper gives an answer to A.F. Sidorov’s question about using functional arbitrariness in study of convergence of the constructed series. There are examples how to prove global convergence by choosing an arbitrary function.