Masayoshi Tajiri

PROPAGATION OF HYDROMAGNETIC WAVES IN COLLISIONLESS PLASMA. II. KINETIC APPROACH.

The propagation of hydromagnetic waves of small amplitude in a collisionless plasma is considered on the basis of the Vlasov equation. It is found that there exist the Alfven wave, the fast and the slow magnetoacoustic waves as well as the non-oscillating mode with vanishing real part of the frequency. Under some conditions, the non-oscillating wave causes the mirror instability in the direction nearly perpendicular to a magnetic field. Numerical discussions are carried out in the phase velocity plane as well as in the Friedrichs diagram for each type of waves, and are compared with the corresponding results in the Chew, Coldberger and Low approximation.

Rarefaction Ion Acoustic Solitons in Two-Electron-Temperature Plasma

This paper shows that rarefaction ion acoustic solitons appear in a two-electron-temperature plasma. And also it presents general conditions and physical mechanism for existence of the rarefaction solitons. It is found that finite amplitude rarefaction and compression solitons coexist in a plasma within a certain parameter region.

Propagation of Hydromagnetic Waves in Collisionless Plasma. I

A collisionless plasma is treated as a hydrodynamical system in the Chew- Goldberger-Low approximation. The dispersion relation for weak, plane disturbances in a uniform plasma is derived. It is shown that the fast and slow magnetoacoustic waves and the Alfven wave exist as well as two degenerate waves that propagate with fluid velocity. The condition such that the system is totally hyperbolic is given, and the configuration for which the system is partially elliptic is investigated in detail especially for the slow wave. (auth)

Similarity Reductions of the One and Two Dimensional Nonlinear Schrödinger Equations

Similarity solutions of the one and two-dimensional nonlinear Schrodinger equations are studied by means of Lies method of infinitesimal transformation groups. It is shown that the two-dimensional nonlinear Schrodinger equation can be reduced to the nonlinear Klein-Gordon equation and others, and the solution of the one-dimensional nonlinear Schrodinger equation for a similarity variable is reducible to the second Painleve transcendent. Some similarity solutions of the equations are obtained.

Precursor of Ion‐Acoustic Quasishock Wave in Collisionless Plasma

A weak, ion‐acoustic quasishock wave which propagates into a uniform state is considered. A relevant initial value problem of the Vlasov equation is solved to give the long time behavior of a precursor which is a stream of ions reflected by the electrostatic potential. An asymptotic expansion in terms of the small amplitude is used. The ratio of the ion temperature to the electron temperature is assumed small so that effects of the reflected ions appear as a correction to the Korteweg‐de Vries equation which governs the wave propagation due to the nonresonant ions. The connection with the stationary solution is examined.

On Large Amplitude Ion Acoustic Solitons in Plasma with Negative Ions

This letter is concerned with existence conditions for ion acoustic solitons in a plasma with negative ions. It is shown that large Mach number potential-well solitons can be in existence in a certain parameter region.

Similarity Solutions of the Kadomtsev-Petviashvili Equation

It is shown that the Kadomtsev-Petviashvili equation can be reduced first to the Boussinesq or Korteweg-de Vries equation, and secondly to the first or second Painleve equation by means of infinitesimal transformations of Lies method. The soliton solutions moving in non-steady and non-uniform background are also obtained.

On N-Soliton Solutions of Coupled Higgs Field Equation

N-soliton solutions of the coupled Higgs field equation are obtained by Hirota bilinear method.

On similarity solutions of the Boussinesq equation

Abstract It is shown that the similarity solutions of the Boussinesq equation satisfy the first or second Painleveequation. We also discuss properties of the soliton solution.

Two-Soliton Resonant Interactions in One Spatial Dimension:Solutions of Boussinesq Type Equation

The soliton solutions of a Boussinesq type equation, u t t - u x x +( u 2 ) x x + u x x x x =0, are analysed to show that the resonant interactions of soliton exist also in one-dimensional propagation. Moreover, the two-soliton interactions of the Ka- domtsev-Petviashvili equation are discussed.