Ginzburg–Landau equations induced from multi-dimensional bichromatic waves

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• 作者：Shuya Kanagawa ; Kiyoyuki Tchizawa ; Takashi Nitta
• 关键词：Ginzburg– ; Landau equation ; Schr&#xf6 ; dinger equation ; Wave equation ; Monochromatic wave ; Bichromatic wave ; Envelope function ; Angular function ; Spectrum function
• 刊名：Nonlinear Analysis
• 出版年：2009
• 出版时间：15 December 2009
• 年：2009
• 卷：71
• 期：12
• 页码：e2258-e2266
• 全文大小：320 K

文摘

In this paper we consider an envelope function for the multi-dimensional bichromatic wave defined by a Fourier transformation and show that it satisfies a kind of Ginzburg–Landau equation under some conditions for the spectrum function and the angular function . The result is an extension of Nohara’s work [B.T. Nohara, Derivation and consideration of governing equations of envelope surface created by directional, nearly monochromatic waves, International Journal of Nonlinear Dynamics and Chaos in Engineering Systems 31 (4) (2003) 375–392; B.T. Nohara, Governing equations of envelope surface created by directional, nearly monochromatic waves, Journal of Japan Society of Industrial and Applied Mathematics 13 (2) (2003) 213–224 (in Japanese)] which treated one-dimensional wave functions.