Particular solitons in nonlinear lattice

One soliton of particle velocity and its amplitude (maximum particle veloci ty of one soliton) in Toda lattice is given analytically It has also been k nown numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define V-n at this time as its maxim um particle velocity) during the collision of two solitons moving in the sa me direction is equal to the difference between the amplitudes of two solit ons if the difference is large enough; however, the maximum particle veloci ty is equal to the adding up of the amplitudes of two solitons moving in th e opposite directions. The relationship between the maximum value of e(-rn) -1 and their initial amplitude of e(-rn) - 1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their m oving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equat ion for solitons during the collision.