Reductive Perturbation Method and Far Fields of Wave Equations (Part I. General Theory)
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概要
- 論文の詳細を見る
The concept of the far field is explained by means of the method of characteristics for the hyperbolic system of nonlinear partial differential equations. The reductive perturbation method is then presented as a method of solution which enables us to reduce a general nonlinear hyperbolic system to a single solvable nonlinear equation describing a far field of the system. The reductive perturbation method applied to more general systmes including dissipation or dispersion shows that for long waves they can be reduced to the Burgers equation or the Kortweg-de Vries equation, respectively. Also, it is shown that a far field for the propagation of slow modulation of a plane wave of infinitesimal amplitude is governed by the Schrodinger equation and that for small but finite amplitudes a general wave system can be reduced to a nonlinear equation of Schrodinger type which we call the generalized nonlinear Schrodinger equation.
- 理論物理学刊行会の論文
- 1975-01-31
著者
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Taniuti Tosiya
Department Of Physics Nagoya University
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Taniuti Tosiya
Department Of Engineering Natural Science-mathematics Chubu University
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