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Two solitons in the same medium.  
Image credit:  Mathematics and 
Statistics at ScholarWorks @UMass 
Amherst (Open Access)

In 1834, naval engineer John Scott Russell was riding his horse along the Union Canal in the Scottish countryside when he made a mathematical discovery.  As he subsequently described it in his “Report on Waves,” presented at a meeting of the British Association for the Advancement of Science in 1844, Russell noticed a boat had stopped abruptly in the canal leaving the water in a state of violent agitation. A large solitary wave emerged from the front of the boat and rolled forward at about eight miles per hour without changing its shape or speed.  He continued on his horse to follow the wave down the canal for nearly two miles until the wave became lost in the winding channel. Russell called this beautiful phenomenon the “wave of translation,” and it has become known as a solitary wave, or soliton.

Russell believed that someday his soliton would be considered fundamentally important in mathematics; he was right.  The first mathematical model of waves on shallow water surfaces, or the Korteweg-de Vries equation, was published years later and became the prototypical textbook nonlinear partial differential equation whose solutions can be unambiguous and exact.  When scientists began using modern digital computers to study non-linear wave propagation, it was discovered that the mathematical and physical theory of the soliton could describe many phenomena in physics, electronics, and biology.  The soliton was later found to be ideal for laser and fiber-optic communications because it retains its identity over distance.  It seems fitting that a fiber-optic cable linking Edinburgh and Glasgow now runs beneath the towpath where Russell discovered the soliton.

Today, scientists at the Department of Energy’s Sandia National Laboratories are among the many researchers utilizing soliton solutions on a wide array of projects.  Juan Elizondo-Decanini leads a project on nonlinear behavior in materials.  Juan developed and patented a detonator comprising a nonlinear transmission line, and he is collaborating with other researchers on potential applications for ultra-wide bandgap materials, micro-sensors, and encryption devices.  DOE research papers involving soliton theory are available in DOE databases.  Related information is also available in William Watson’s latest white paper “Solitons” and in OSTI’s July 2016 Science Showcase featuring Solitons.