ABSTRACT
As we increasingly turn to nonlinear models to capture some of the more salient behavior of physical or natural systems that cannot be expressed by linear means, systems that support solitons may be a natural class to explore because they share many of the properties that make linear time-invariant (LTI) systems attractive from an engineering standpoint. Although nonlinear, these systems are solvable through inverse scattering, a technique analogous to the Fourier transform for linear systems [1]. Solitons are eigenfunctions of these systems which satisfy a nonlinear form of superposition. We can therefore decompose complex solutions in terms of a class of signals with simple dynamical structure. Solitons have been observed in a variety of natural phenomena from water and plasma waves [7,12] to crystal lattice vibrations [2] and energy transport in proteins [7]. Solitons can also be found in a number of manmade media including superconducting transmission lines [11] and nonlinear circuits [6,13]. Recently, solitons have become of significant interest for optical telecommunications, where optical pulses have been shown to propagate as solitons for tremendous distances without significant dispersion [4].
