WHAT IS A SOLITON?
In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (The term "dispersive effects" refers to a property of certain systems where the speed of the waves varies according to frequency). Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems.
The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". Read more in Wikipedia
We examine the evolution of a time-varying perturbation signal pumped into a monomode fiber in the anomalous dispersion regime. We establish analytically that the perturbation evolves into a conservative pattern of periodic pulses whose structures and profiles share a close similarity with the so-called soliton-crystal states recently observed in fiber media [see, e.g., A. Haboucha et al., Phys. Rev. A 78, 043806 (2008); D. Y. Tang et al., Phys. Rev. Lett. 101, 153904 (2008); F. Amrani et al., Opt. Express 19, 13134 (2011)]. We derive mathematically and generate numerically a crystal of solitons using time-division multiplexing of identical pulses. We suggest that at very fast pumping rates, the pulse signals overlap and create an unstable signal that is modulated by the fiber nonlinearity to become a periodic lattice of pulse solitons that can be described by elliptic functions. We carry out a linear stability analysis of the soliton-crystal structure and establish that the correlation of centers of mass of interacting pulses broadens their internal-mode spectrum, some modes of which are mutually degenerate. While it has long been known that high-intensity periodic pulse trains in optical fibers are generated from the phenomenon of modulational instability of continuous waves, the present study provides evidence that they can also be generated via temporal multiplexing of an infinitely large number of equal-intensity single pulses to give rise to stable elliptic solitons.