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Local solutions of the Kadomtsev-Petviashvili equation
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| 其它 | 作者：Ukai, S.期刊名：Journal of the Faculty of Science. Section I A年份：1989卷号：Vol.36期号：No.2页码：193-209I S S N：0040-8980关键词：Cauchy problem; Kadomtsev-Petviashvili equation; Sobolev space本科生分类：20 ( 综合 )研究生分类：20 ( 综合 )摘要：The author considers a Cauchy problem of the Kadomtsev-Petviashvili equation (U t +αUU x +βU xxx ) x +γU yy =0, where U=U(t,x,y) is a scalar unknown function and α, β, γ are real constants. The main purpose of this paper is to construct a local (in time) solution of KP equation for initials small in the Sobolev space W 2,s (Ω) with s≥3 and a certain restriction. As for domain Ω, the author deals with four cases ℝ 2 , ℝ×핋, 핋×ℝ and 핋 2 where 핋 is a one-dimensional torus. The existence of solutions is established by using general local theory for the quasilinear symmetric hyperbolic system. The proofs are given in detail |
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