# Graduate School in Nonlinear Science

**
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
**

**THE HAMILTON DYNAMICS OF THE SOLITON OF THE DISCRETE NLS EQUATION **

**by Professor Arnold M. Kosevich**

B. Verkin Institute for Low Temperature Physics
and Engineering

of National Academy of Sciences of Ukraine

310164 Kharkov

Ukraine

email: kosevich@ilt.kharkov.ua

MIDIT-seminar 514

**Tuesday, November 5, 2002, 14.00 h**

at IMM, Bldg. 305, Room 053, DTU

**Abstract:**
Hamiltonian equations are formulated in terms of collective variables
describing the dynamics of the soliton of an integrable NLS equation on a 1D
lattice. Earlier, similar equations of motion were sugested for the soliton
of the NLS equation in partial derivatives. The operator of soliton momentum
in a discrete chain is defined; this operator is unambigously related to the
velocity of the center of gravity of the soliton. The resulting Hamiltonian
equations are similar to those for the continuous NLS equation, but the role
of the field momentum is played by the summed quasi-momentum of virtual
elemrntary system excitations related to the soliton.