A Model of the Dispersive Non-Linear Equation

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概要

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• In this paper we consider a model of the dispersive non-linear equation which is derived from the Schrodinger equation by means of a non-linear transformation. The derivation is closely analogous to deriving the Burgers model from the diffusion equation. Then we obtain a solution resulting from an initial discontinuity, which corresponds to that of Riemann's problem in the Burgers model. In the solution so obtained, the limit that the Planck constant vanishes is discussed in comparison with the dissipative limit in the Burgers model which is realized by letting the dissipation constant tend to zero. It is explicitly shown that although in these limits the equations in the two models are the same, nevertheless their solutions are entirely different; for example, as is well known, in the Burgers model one discontinuity develops from the initial discontinuity while in our model two discontinuities develop, across each of which the so-called generalized Rankine-Hougoniot relations are not valid.

• 理論物理学刊行会の論文
• 1966-06-25

著者

• TANIUTI Tosiya

  Institute of Plasma Physics, Nagoya University

• OUTI Akizi

  Institute of Plasma Physics, Nagoya University

• Outi Akizi

  Institute Of Plasma Physics Nagoya University

• Outi Akizi

  Institute Of Physical And Chemical Research

• YAJIMA Nobuo

  Institute of Plasma Physics, Nagoya University

• Yajima Nobuo

  Institute Of Plasma Physics Nagoya University

• Taniuti Tosiya

  Institute Of Plasma Physics Nagoya University

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• Particle Orbits in a Heliotron Magnetic Field
• A New Example of Stable Solitary Waves
• A Model of the Dispersive Non-Linear Equation
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• Resonant Interaction of Solitons and Zakharov-Shabat Theory
• A Model of the Dispersive Non-Linear Equation. II
• Non-Linear Motion of Ion Streams in a Background of High Temperature Electrons
• Analysis of the High Energy Jet Showers. III : Analysis of Experimental Data
• Motion of Charged Particles Confined in a Helically Invariant Magnetic Field
• Analysis of the High Energy Jet Showers. I : A Proposal of New Kinematics
• Analysis of the High Energy Jet Showers. II : Monte Carlo Test of the New Formulae
• Analysis of the High Energy Jet Showers. I : A Proposal of New Kinematical Approach
• The Effect of Finite Ion Larmor Radius on the Alfven Wave Instability
• Application of Linear Response Theory to Dielectric and Conduction Problems in a Turbulent Plasma
• Propagation of Hydromagnetic Waves in a Collisionless Plasma
• The Effect of Finite Ion Larmor Radius on the Propagation of Magnetoacoustic Waves

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