passage of each wave, and a distinct wave crest and wave trough are evident. A 

 solitary wave is neither oscillatory nor does it exhibit a trough. In the 

 pure sense, the solitary waveform lies entirely above the Stillwater level. 

 The solitary wave is a wave of translation relative to the water mass. 



The first systematic observations and experiments on waves can probably be 

 attributed to Russell (1838, 1844). Russell first recognized the existence of 

 a solitary wave, and the report (Russell, 1844) of his first observation is 

 worth noting. 



"I believe I shall best introduce this phenomenon by describ- 

 ing the circumstances of my own first acquaintance with it. I 

 was observing the motion of a boat which was rapidly drawn 

 along a narrow channel by a pair of horses, when the boat 

 suddenly stopped — not so the mass of water in the channel 

 which it had put in motion; it accumulated round the prow of 

 the vessel in a state of violent agitation, then suddenly 

 leaving it behind, rolled forward with great velocity, assum- 

 ing the form of a large solitary elevation, a rounded, smooth 

 and well-defined heap of water, which continued its course 

 along the channel apparently without change of form or dimin- 

 uation of speed. I followed it on horseback, and overtook it 

 still rolling on at a rate of some eight or nine miles an 

 hour, preserving its original figure some thirty feet long 

 and a foot to a foot and a half in height. Its height grad- 

 ually diminished, and after a chase of one or two miles I 

 lost it in the windings of the channel. Such, in the month 

 of August 1834, was my first chance interview with that 

 singular and beautiful phenomenon which I have called the 

 Wave of Translation, a name which it now very generally 

 bears ; which I have since found to be an important element in 

 almost every case of fluid resistance, and ascertained to be 

 the type of that great moving elevation of the sea, which, 

 with the regularity of a planet, ascends our rivers and rolls 

 along our shores. 



"To study minutely this phenomenon with a view to determine 

 accurately its nature and l=iws, I have adopted other more 

 convenient modes of producing it than that which I have just 

 described, and have employed various methods of observation. 

 A description of these will probably assist me in conveying 

 just conceptions of the nature of this wave." 



The study of waves developed from this chance observation in 1834. While 

 Russell's studies were empirical in nature, his results agree well with later 

 theoretical results. The original theoretical developments were made by 

 Boussinesq (1872) Rayleigh (1876), and McCowan (1891), and more recently by 

 Keulegan and Patterson (1940), Keulegan (1948), and Iwasa (1955). 



In nature it is difficult to form a truly solitary wave, because at the 

 trailing' edge of the wave there are usually small dispersive waves. However, 

 long waves such as tsunamis and waves resulting from large displacements of 

 water caused by such phenomena as landslides and earthquakes sometimes behave 

 approximately like solitary waves. When an oscillatory wave moves into 



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