On a Method for Solving of Multidimensional Equations of Mathematical Physics

We consider linear multidimensional evolutionary equations or the linear part of nonlinear ones. The complex structure and the presence of terms with different physical sense requires the coordinate splitting to be preceded by splitting by physical factors (processes). In contrast to the coordinate splitting this kind of splitting can be exact in some nodes and in the intervals it can be controlled. The method in question is developed in 80s of 20th century by G. Marchuk [1] and till now it is applied very successfully for solving various problems in ecology, air and water pollution, diffusion, etc. Here we show that this method is relevant for studying of propagating ultrashort localized pulses in nonlinear waveguides as well