This work deals with the probability solution structure for some stochastic equations as the dynamic foundation for statistic generation on the base of functional methods. At the first step, the general methodology is formed for the characteristic functionals (ChF) determining in the case of non-linear dynamic problem solutions in terms of the ChF of external action (source). This method is used for concluding the statistics of solutions for definite class of non-linear equations in space-time-domain, whereas satisfied to cause conditions. Then this method is distributed on one-dimension non-linear wave equation. Finally, the analytical forms are constructed for ChF of the solutions in terms of ChF of external random sources for hydrophisical and hydroacoustic channels for information propagation.