Representation of solutions of nonlinear evolution equations in the form of special series with recurrent calculating coefficients

Abstract

By using of a method of special series a class of solutions with a functional arbitrariness is constructed for equations of evolution type. The coefficients of the series are constructed in explicit form as a sequence of solutions of first order linear ordinary differential equations. Convergence of the constructed series is proved in a semi-infinite region, and the functional arbitrariness included in the constructed solution allows to use these series to prove solvability of initial-boundary value problems.