Kazuhiro Nozaki

Exact Solutions of the Generalized Ginzburg-Landau Equation

It is shown that the 1-D generalized Ginzburg-Landau equation has a solitary wave solution, a hole solution and a shock-type solution. In the absence of a linear dispersion, we have another exact solution showing that the collision of two shock-type waves results in the formation of the hole.

Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation

Abstract A new exact propagating-hole solutionis obtained in the generalized Ginzburg-Landau equation and a phase-jump in the hole is shown to generate definite spatial patterns in a stable homogeneous state.

Low-dimensional chaos in a driven damped nonlinear Schro¨dinger equation

Abstract We study bifurcations of attractors in a driven damped nonlinear Schrodinger equation, which models nonlinear responses of a plasma driven by a rf field and a sequence of period-doubling bifurcations is shown to lead to a chaotic attractor in a low-dimensional subspace spanned by a soliton and long-wavelength radiation.

Propagation of Solitary Pulses in Interactions of Plasma Waves

New solutions of solitary pulses in three-wave interactions are obtained, which were not given in the previous paper of this series. In those solutions, the wave of lower frequency has a shock-type envelope and behaves as a “pump” while the other two waves have the pulse-type ones. In addition, by considering two effects, linear translations of the waves and nonlinear interactions, a physical mechanism of formation of the solitary pulses is found. The theory is applied to the interaction among two Alfven waves and an ion-acoustic wave, which propagate along the external magnetic field,

Hirota's Method and the Singular Manifold Expansion

A system of equations u t +( u 2 /2-α u m x +β u n x ) x =0 ( m , n : positive integers, β≠0) is studied by means of Hirotas method and the singular manifold expansion. The singular manifold expansion yields the transformation of the system into bilinear forms or higher order ones and we obtain some explicit solutions of the system in physically interesting but non-integrable cases.

Solitons as attractors of a forced dissipative nonlinear Schrödinger equation

Abstract A single soliton and a bound state of two solitons are shown to be approximate simple or strange attractors of a forced dissipative nonlinear Schrodinger equation when forcing and dissipative terms are small.

Chaotic Solitons in a Plasma Driven by an rf Field

A sequence of period-doubling bifurcations is shown to lead to a chaotic attractor in a low dimensional subspace spanned by a soliton and long-wavelength radiation of an infinite dimensional system, which models nonlinear responses of a plasma driven by a capacitor rf field.

Solitons in a Convective Motion of a Low-β Plasma

The present paper shows that in a plane normal to an applied magnetic field, envelope solitary vortices comprising convective cells of small scale propagate through a nonuniform bounded plasma of low β as envelope solitons of a nonlinear Schrodinger equation. It is shown further that the modulational instability is enhanced resonantly for certain wavenumbers and vortices of large scale is excited by the ponderomotive force. Discussions are based on the model equation of Hasegawa and Mima that is the geostrophic vortex equation, and a generation of zonal flows by the Rossby wave is noted.

Lie-Group Approach to Perturbative Renormalization-Group Method

A new Lie-group approach to the perturbative renormalization group (RG) methodis developed to obtain asymptotic solutions of both autonomous and non-autonomous ordinary differential equations. Reduction of some partial differential equations to typical RG equations is also achievedwith this approach, anda simple recipe for provid ing RG equations is presented.

Propagation of Drift Waves of Small but Finite Amplitude

It is shown that the drift wave of small but finite amplitude propagating in a plasma of hot electrons and cold ions is governed by a modified Kortweg-de Vries equation in two-dimensional space comprising the external magnetic field and the direction normal to a density gradient. The solitary wave is obtained explicitly.