<title>Methods of small parameter approximation in analyzing the propagation and interaction of soliton-like pulses</title>

Abstract

Possibility of deriving of approximated solutions of the nonlinear Schrodinger equation (NSE) is presented, using the Bogol'ubov's method of small parameter. Following the restrictions of first-approximation solutions, we obtain the ordinary differential equations system, which describes the temporal dependence of amplitudes, velocities, positions and phases of weak-interacting solitons. We consider that the ε small parameter method facilitates the application into analysis, when comparing with the method of scattering inverse task. The Bogol'ubov's ε parameter method gives the possibility to obtain the NSE solutions even in high order approximations, as well. Thus, the accuracy of calculations increases when studying the evolution of the interaction of soliton-like pulses.