Nonlinear lattice and soliton theory

Since the notion of stable pulses, known as solitons, plays a central role in the phenomena of wave propagation in nonlinear systems, an exposition of this topic is developed in some detail. It is known that the equations of motion of the one-dimensional lattice of particles with exponential interaction are integrable, namely, they admit exact solutions, and this system is equivalent to an circuit with certain nonlinear capacitance. In addition, a closely related partial differential equation called the Korteweg-de Vries (KdV) equation is also integrable. Special emphasis is placed on these integrable systems.