Soliton-like waves on dissipative Toda lattices

Dissipative soliton-like waves in 1D Toda lattices generated by suitable en ergy supply from external sources have been studied. Using the general theo ry of canonical-dissipative systems we have constructed a special canonical -dissipative system whose solution starting from an arbitrarily initial con dition decays to a solution of the standard, conservative Toda system. The energy of the final state may be prescribed beforehand. We have also studie d the influence of noise and have calculated the distribution of probabilit y density in phase space and the energy distribution. Other noncanonical mo dels of energy input, including nonlinear nearest neighbor coupling and "Ra yleigh" friction, have been analyzed. We have shown under what conditions t he lattices can sustain the propagation of stable solitary waves and wave t rains.