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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 Novikov–Veselov equation ： ウィキペディア英語版 Novikov–Veselov equation In mathematics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a natural (2+1)-dimensional analogue of the Korteweg–de Vries (KdV) equation. Unlike another (2+1)-dimensional analogue of KdV, the Kadomtsev–Petviashvili equation, it is integrable via the inverse scattering transform for the 2-dimensional stationary Schrödinger equation. Similarly, the Korteweg–de Vries equation is integrable via the inverse scattering transform for the 1-dimensional Schrödinger equation. The equation is named after S.P. Novikov and A.P. Veselov who published it in . ==Definition== The Novikov–Veselov equation is most commonly written as where $v\; =\; v(\; x\_1,\; x\_2,\; t\; ),$ $w\; =\; w(\; x\_1,\; x\_2,\; t\; )$ and the following standard notation of complex analysis is used: $\backslash Re$ is the real part, :$$ \partial_ = \frac ( \partial_ - i \partial_ ), \quad \partial_ = \frac ( \partial_ + i \partial_ ). The function $v$ is generally considered to be real-valued. The function $w$ is an auxiliary function defined via $v$ up to a holomorphic summand, $E$ is a real parameter corresponding to the energy level of the related 2-dimensional Schrödinger equation :$$ L \psi = E \psi, \quad L = - \Delta + v( x, t ), \quad \Delta = \partial_^2 + \partial_^2. 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「Novikov–Veselov 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.