Representation of solutions of boundary value problems for nonlinear evolution equations by special series with recurrently calculated coefficients

One of the analytical methods of presenting solutions of nonlinear partial differential equations is the method of special series in powers of specially selected functions called basic functions. The coefficients of such series are found successively as solutions of linear differential equations. The basic functions can also contain arbitrary functions. By using such functional arbitrariness allows in some cases, to prove the global convergence of the corresponding constructed series, and also allows us to prove the solvability of the boundary value problem for the Korteweg-de Vries equation. In the paper for a nonlinear wave equation a theorem on the possibility of satisfying a given boundary condition using an arbitrary function contained in the basic function is proved.