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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- Chong Song
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Email: email@example.com
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 140 (2012), 635-644
- MSC (2010): Primary 37K25, 58E50, 53C99
- DOI: https://doi.org/10.1090/S0002-9939-2011-10930-4
- MathSciNet review: 2846333