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Solitons and the Korteweg-de Vries equation: Integrable systems in 1834–1995

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Abstract

We trace the connections back from the paper by D. J. Korteweg and G. de Vries of 1895 to the sequence of events which began in August 1834 when J. S. Russell observed the soliton and so explain why KdV's paper was so much concerned with ‘change of form of long waves’. From this we trace a forward path which since 1895 has seen the discovery of the inverse method, associated with this a far-reaching mathematical structure, and at 1995 found a basis for two-dimensional quantum gravity intimately connected with the Korteweg-de Vries equation.

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  1. Department of Mathematics, UMIST, PO Box 88, M60 1QD, Manchester, UK

    R. K. Bullough & P. J. Caudrey

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Bullough, R.K., Caudrey, P.J. Solitons and the Korteweg-de Vries equation: Integrable systems in 1834–1995. Acta Appl Math 39, 193–228 (1995). https://doi.org/10.1007/BF00994634

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