The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrodinger equation

Hamiltonian equations are formulated in terms of collective variables descr ibing the dynamics of the soliton of an integrable nonlinear Schrodinger eq uation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrodinger equation in partial derivativ es. The operator of soliton momentum in a discrete chain is defined; this o perator is unambiguously related to the velocity of the center of gravity o f the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrodinger equation, but the role of the field m omentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton. (C) 2001 MAIK "Nauka/Interperiodica".