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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The KdV curve and Schrödinger-Airy curve
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by Chong Song PDF
Proc. Amer. Math. Soc. 140 (2012), 635-644 Request permission

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
  • Email: songchong@amss.ac.cn
  • 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