On a New Series of Integrable Nonlinear Evolution Equations
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概要
- 論文の詳細を見る
Recent results of our research are surveyed in this report. The derivative nonlinear Schrodinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schrodinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schrodinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schrodinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discreet. It is a new challenge to construct singular potentials by the inverse scattering transformation.
- 核融合科学研究所の論文
著者
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Ichikawa Yoshi
Research Information Center Institute Of Plasma Physics Nagoya University:institute Of Plasma Physic
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Wadati Miki
Institue Of Applied Physics Tsukuba University
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Konno Kimiaki
Research Information Center, Institute of Plasma Physics, Nagoya University
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Wadati Miki
Research Information Center, Institute of Plasma Physics, Nagoya University
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Shimizu Tohru
Research Information Center, Institute of Plasma Physics, Nagoya University
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Konno Kimiaki
Research Information Center Institute Of Plasma Physics Nagoya University:department Of Physics Coll
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Ichikawa Yoshi
Research Information Center Institute Of Plasma Physics Nagoya University
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Shimizu Tohru
Research Center For Space And Cosmic Evolution Ehime University
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Shimizu Tohru
Research Information Center Institute Of Plasma Physics Nagoya University:institute Of Physics Unive
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Wadati Miki
Research Information Center Institute Of Plasma Physics Nagoya University:department Of Physics And
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KONNO Kimiaki
Department of Physics, College of Science and Technology Nihon University
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ICHIKAWA YOSHI
Institute of Plasma Physics, Nagoya University
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