Solitary Wave in Periodic Nonlinear Lattice

Abstract

The behaviour of solitary wave has been studied numerically in periodic Toda lattice which has alternate Toda potentials with different parameters. In the numerical calculation, due to deviations from the ideal Toda lattice, the solitary wave decreases in propagation, trailing ripple oscillation behind it. Yet, the stability of the waves depends on the lattice parameters. A narrow solitary wave compared with the lattice constant can propagate stably in the periodic lattice under our special condition. The validity of the K-dV approximation is examined concerning the velocity and width of a small amplitude solitary wave. The duality of nonlinear lattice is also discussed.