Abstract
Many of the equations which now are called integrable have been known in differential geometry for a long time. Probably the first was the famous sine-Gordon equation, which was derived to describe surfaces with constant negative Gaussian curvature. At that time many features of integrability of the sine-Gordon and other integrable equations were discovered 1, namely those which have clear geometrical interpretation (for example, the Bäcklund transform).
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Bobenko, A.I. (1994). Surfaces in terms of 2 by 2 matrices. Old and new integrable cases. In: Fordy, A.P., Wood, J.C. (eds) Harmonic Maps and Integrable Systems. Aspects of Mathematics, vol E 23. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14092-4_5
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DOI: https://doi.org/10.1007/978-3-663-14092-4_5
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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