Exact Description of the Discrete Breathers and Solitons Interaction in the Nonlinear Transmission Lines

Abstract

For the nonlinear self-dual network equations and the equivalent Hirota lattice equation the pair collision processes of two discrete breathers, breather and one-parametric soliton (kink, antikink), breather and linear wave, one-parametric soliton and linear wave are described. The explicit expressions of the “kink-breather” and “breather-breather” solutions are constructed. The shifts of the center-of-masses and phases of the breather oscillations have been expressed in terms of the dynamical characteristics of linear and nonlinear excitations of the system.