Laptiev D. Dynamics of discrete breathers in integrable models of crystal and electric systems

Dissertation is devoted to theoretical research of the dynamics of the discrete breathers in the frame of the Hirota lattice model and the equivalent system of self-dual network equations. It is shown that these excitations elastically interact with each other and with shock and linear waves. The Hamiltonian equations and quasiclassical spectra for the discrete breathers and kinks as the particle-like excitations of the Hirota lattice are found. For the first time exact nonlinear periodic solutions describing the breathers and solitons superlattices in electric transmission line and the Hirota lattice are found, and their stability boundaries are determined.