Proceedings of the American Mathematical Society

The initial value problem for a third order dispersive equation on the two-dimensional torus

Author(s): Hiroyuki Chihara
Journal: Proc. Amer. Math. Soc. 133 (2005), 2083-2090.
MSC (2000): Primary 35G10
Posted: January 31, 2005
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Abstract: We present the necessary and sufficient conditions for the

-well-posedness of the initial problem for a third order linear dispersive equation on the two-dimensional torus. Birkhoff's method of asymptotic solutions is used to prove necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play a crucial role in proving sufficiency.

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Hiroyuki Chihara
Affiliation: Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
Email: chihara@math.tohoku.ac.jp

DOI: 10.1090/S0002-9939-05-07783-X
PII: S 0002-9939(05)07783-X
Received by editor(s): March 16, 2004
Posted: January 31, 2005
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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