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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Regularized long-wave equation ： ウィキペディア英語版 Benjamin–Bona–Mahony equation The Benjamin–Bona–Mahony equation (or BBM equation) – also known as the regularized long-wave equation (RLWE) – is the partial differential equation :$u\_t+u\_x+uu\_x-u\_=0.\backslash ,$ This equation was studied in as an improvement of the Korteweg–de Vries equation (KdV equation) for modeling long surface gravity waves of small amplitude – propagating uni-directionally in 1+1 dimensions. They show the stability and uniqueness of solutions to the BBM equation. This contrasts with the KdV equation, which is unstable in its high wavenumber components. Further, while the KdV equation has an infinite number of integrals of motion, the BBM equation only has three. Before, in 1966, this equation was introduced by Peregrine, in the study of undular bores. A generalized ''n''-dimensional version is given by :$u\_t-\backslash nabla^2u\_t+\backslash operatorname\backslash ,\backslash varphi(u)=0.\backslash ,$ where $\backslash varphi$ is a sufficiently smooth function from $\backslash mathbb\; R$ to $\backslash mathbb\; R^n$. proved global existence of a solution in all dimensions. ==Solitary wave solution== The BBM equation possesses solitary wave solutions of the form:〔 :$u\; =\; 3\; \backslash frac\; \backslash operatorname^2\; \backslash frac12\; \backslash left(\; cx\; -\; \backslash frac\; +\; \backslash delta\; \backslash right),$ where sech is the hyperbolic secant function and $\backslash delta$ is a phase shift (by an initial horizontal displacement). For , the solitary waves have a positive crest elevation and travel in the positive $x$-direction with velocity $1/(1-c^2).$ These solitary waves are not solitons, i.e. after interaction with other solitary waves, an oscillatory tail is generated and the solitary waves have changed.〔〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Benjamin–Bona–Mahony equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.