Numerical simulation of soliton solutions of simples discrete equations and their continual limits

A sequence of discrete equations with the Bogoyavlensky's integral kinetic equation and KdV equation in their continual limits is considered. The general algorithm of their solutions is investigated. Integration by time is provided by the Runge–Kutta fourth-order method, integral and differential terms are calculated with the help of Fourier transformation. Soli ton solutions for the unsteady discrete equations are found, their individual properties are determinated. Features of the typical solitons interaction are described. One- and two- soliton solutions of the Bogoyavlensky's integral kinetic equation are found.