Analytical and numerical peculiarities of solving nonlinear problems are con-sidered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equa-tion (KPI). KPI is represented in integro-differential form. Main attention is paid to theproblem of asymptotical behavior of solution and appearance of nonphysical artefacts.The numerical solution is carried out by the finite difference method. For a correct rep-resentation of the boundary condition along theyaxis in numerical simulation a methodis proposed for introducing small artificial convection into the original equation in theindicated direction. Along with the introduction of artificial convection, the procedure oftrimming of the integral on the bands adjacent to the upper and lower boundaries of thecalculated region is used. The results obtained by numerical testing, showed sufficientaccuracy and validity of this procedure.