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The KdV curve and Schrödinger-Airy curve

Author: Chong Song
Journal: Proc. Amer. Math. Soc. 140 (2012), 635-644
MSC (2010): Primary 37K25, 58E50, 53C99
Published electronically: June 17, 2011
MathSciNet review: 2846333
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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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Additional Information

Chong Song
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China

Received by editor(s): October 22, 2010
Received by editor(s) in revised form: November 28, 2010, and December 2, 2010
Published electronically: June 17, 2011
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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