The KdV curve and Schrödinger-Airy curve

Song, Chong

doi:10.1090/S0002-9939-2011-10930-4

The KdV curve and Schrödinger-Airy curve
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by Chong Song

Proc. Amer. Math. Soc. 140 (2012), 635-644

DOI: https://doi.org/10.1090/S0002-9939-2011-10930-4

Published electronically: June 17, 2011

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Abstract:

Among other things, we introduce the notion of KdV curves and Schrödinger-Airy curves. These curves are stable solutions to the geometric KdV-Airy flow equation and Schrödinger-Airy flow equation respectively, which were recently proposed by Sun and Wang. We demonstrate that the KdV curves can be regarded as a 3rd-order analogue of geodesics. Other interesting properties of these curves will be addressed. Explicit examples of these curves will be provided. In addition, we will consider a perturbed KdV curve system and show the existence of multiple solutions to this system on the torus.

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