Theoretical study of lattice solitons in nonlinear lumped networks

Abstract

An analytical solution of the equation of motion in an anharmonic one-dimensional lattice was found by toda. An equivalent solution for a nonlinear lumped LC network was derived as an analogue for the anharmonic one-dimensional lattice. The fundamental properties of solitons were verified. These properties include: (1) the dependence of the amplitude of a single soliton on the velocity of propagation, (2) the emergence of two solitons after collision without changing their shapes, and (3) the conservation of the voltage and power integrals with respect to a normalized time.