Ultra-wideband analogue channels using solitons
It is shown that the dynamics of N-solitons of the Korteweg-de Vries (KdV) equation can be reduced to the Toda lattice equations for the temporal positions of the solitons when the solitons are nearly identical and widely separated in time. Invariants of the KdV equation map to corresponding invariants of the Toda lattice, and the map exists in the limit N/spl rarr//spl infin/. These invariants form analogue channels for the communication of data in which an exact memory of the initial conditions is preserved, even though the KdV wavetrain itself is evolving dynamically. It follows that there exist channels which are immune to the effects of the interpulse dynamics in the KdV wavetrain.