OSTIblog Articles in the Solitons Topic

The Soliton: A Solitary Wave that Retains Its Identity over Distance

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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...

Related Topics: solitary wave, Solitons