On the Existence of Periodic Travelling Wave Solutions to Nonlinear Dispersive Equations

Material type: 文書・図像類

Author: 岩宮, 敏幸ほか

Publisher: 航空宇宙技術研究所

Publication date: 1980-09

Material Format: Digital

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Note (General)：: 本稿では,Kortweg-de Vries 方程式Ut+UUx+Uxxx=0及び正則化された長波方程式Ut+Ux+UUx-Uxxt=0を含む非線形分散方程式Ut+(φ(U))x+δUxxx-∈Uxxt=0の次の形の解U(t,x)=w(x-ct)即ち,周期的進行波解の存在問題を論じる。ここでは,周期的...

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Material Type: 文書・図像類
Title: On the Existence of Periodic Travelling Wave Solutions to Nonlinear Dispersive Equations
Author/Editor: 岩宮, 敏幸
高橋, 匡康
IWAMIYA, Toshiyuki
TAKAHASHI, Tadayasu
Author Heading: 岩宮, 敏幸
高橋, 匡康
IWAMIYA, Toshiyuki
TAKAHASHI, Tadayasu
Publication, Distribution, etc.: 航空宇宙技術研究所
Publication Date: 1980-09
Publication Date (W3CDTF): 1980-09
Periodical title: 航空宇宙技術研究所報告 = Technical Report of National Aerospace Laboratory TR-625T
No. or year of volume/issue: 625T
Volume: 625T
Pages: 7-
ISSN (Periodical Title): ISSN : 0389-4010
Text Language Code: eng
Target Audience: 一般
Note (General): 本稿では,Kortweg-de Vries 方程式Ut+UUx+Uxxx=0及び正則化された長波方程式Ut+Ux+UUx-Uxxt=0を含む非線形分散方程式Ut+(φ(U))x+δUxxx-∈Uxxt=0の次の形の解U(t,x)=w(x-ct)即ち,周期的進行波解の存在問題を論じる。ここでは,周期的進行波解の存在問題を常微分方程式の周期解の存在問題に帰着させ,周期的進行波解が存在するための条件を与えるとともに,解の積分表示をも与える。さらに,正則化された長波方程式については,その周期的進行波解が,Weierstrassのペー(ρ)関数によって表示されることを示す。
This paper is concerned with the existence of periodic travelling wave solutions to some nonlinear dispersive equations which are modified versions of the Kortweg-de Vries equation. The existence problem is reduced to the problem of finding periodic solutions of a certain kind of ordinary differential equation and the solvability of the reduced problem is studied in detail. By applying the result obtained for the reduced problem to the original problem, conditions for the existence(as well as the nonexistence)of the periodic travelling waves are derived. Furthermore, it is shown that the travelling wave solutions of the regularized wave equation are represented by means of the Weierstrass functions.
資料番号: NALTR0625T000
レポート番号: NAL TR-625T
Access Restrictions: 限定公開
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 宇宙航空研究開発機構 : 宇宙航空研究開発機構リポジトリ