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

2004/04/01 by Hiroyuki Chihara, Chihara, Hiroyuki
Mathematics · Physics and Astronomy · #35G10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.AP #math.CA #msc:35G10

paper · pdf · doi:10.48550/arxiv.math/0404006

7 pages, no figure

openalex publication_date 2004/04/01 · arxiv created 2004/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the necessary and sufficient condition for the L²-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 the necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play crucial role in proving the sufficiency.

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