翻訳と辞書 Words near each other ・ Vakati Panduranga Rao ・ Vake ・ Vake (Gagra District) ・ Vake Park ・ Vakeeswarar ・ Vakfıkebir ・ Vakfıkebir Arena ・ Vakfıkebir bread ・ Vakh River ・ Vakha Albakov ・ Vakha Arsanov ・ Vakha Keligov ・ Vakhid Masudov ・ Vakhid Tsartsayev ・ Vakhitov ・ Vakhitov–Kolokolov stability criterion ・ Vakhmistrov I-Ze ・ Vakhrushev ・ Vakhrusheve ・ Vakhrushevo ・ Vakhsh ・ Vakhsh District ・ Vakhsh Qurghonteppa ・ Vakhsh Range ・ Vakhsh River ・ Vakhsh, Tajikistan ・ Vakhshak ・ Vakhtang ・ Vakhtang Ananyan ・ Vakhtang Balavadze Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Vakhitov–Kolokolov stability criterion ： ウィキペディア英語版 Vakhitov–Kolokolov stability criterion The Vakhitov–Kolokolov stability criterion is a condition for linear stability (sometimes called ''spectral stability'') of solitary wave solutions to a wide class of U(1)-invariant Hamiltonian systems, named after Russian scientists Aleksandr Kolokolov (Александр Александрович Колоколов) and Nazib Vakhitov (Назиб Галиевич Вахитов). The condition for linear stability of a solitary wave $u(x,t)=\backslash phi\_\backslash omega(x)e^\backslash ,$ with frequency $\backslash omega\backslash ,$ has the form :$$ \fracQ(\omega)<0, where $Q(\backslash omega)\backslash ,$ is the charge (or momentum) of the solitary wave $\backslash phi\_\backslash omega(x)e^\backslash ,$, conserved by Noether's theorem due to U(1)-invariance of the system. ==Original formulation== Originally, this criterion was obtained for the nonlinear Schrödinger equation, :$$ i\fracu(x,t)=-\frac u(x,t)+g(|u(x,t)|^2)u(x,t), where $x\backslash in\backslash R\backslash ,$, $t\backslash in\backslash R$, and $g\backslash in\; C^\backslash infty(\backslash R)$ is a smooth real-valued function. The solution $u(x,t)\backslash ,$ is assumed to be complex-valued. Since the equation is U(1)-invariant, by Noether's theorem, it has an integral of motion, $Q(u)=\backslash frac\backslash int\_|u(x,t)|^2\backslash ,dx$, which is called charge or momentum, depending on the model under consideration. For a wide class of functions $g\backslash ,$, the nonlinear Schrödinger equation admits solitary wave solutions of the form $u(x,t)=\backslash phi\_\backslash omega(x)e^\backslash ,$, where $\backslash omega\backslash in\backslash R$ and $\backslash phi\_\backslash omega(x)\backslash ,$ decays for large $x\backslash ,$ (one often requires that $\backslash phi\_\backslash omega(x)\backslash ,$ belongs to the Sobolev space $H^1(\backslash R^n)$). Usually such solutions exist for $\backslash omega\backslash ,$ from an interval or collection of intervals of a real line. Vakhitov–Kolokolov stability criterion, :$$ \fracQ(\phi_\omega)<0, is a condition of spectral stability of a solitary wave solution. Namely, if this condition is satisfied at a particular value of $\backslash omega\backslash ,$, then the linearization at the solitary wave with this $\backslash omega\backslash ,$ has no spectrum in the right half-plane. This result is based on an earlier work by Vladimir Zakharov. 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「Vakhitov–Kolokolov stability criterion」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.