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Third order semilinear dispersive equations related to deep water waves

Hiroyuki Chihara
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Abstract

We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and cannot be solved by the classical energy method. To solve the initial value problem, we make full use of pseudodifferential operators with nonsmooth coefficients.

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Hiroyuki Chihara. 2004-07-27. Third order semilinear dispersive equations related to deep water waves. https://arxiv.org/abs/math/0404005

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