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

Chihara, Hiroyuki

doi:10.1090/S0002-9939-05-07783-X

The initial value problem for a third order dispersive equation on the two-dimensional torus
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Proc. Amer. Math. Soc. 133 (2005), 2083-2090 Request permission

Abstract:

We present the necessary and sufficient conditions for the $L^2$-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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