Miki Wadati

Dark Solitons in F=1 Spinor Bose–Einstein Condensate

We study dark soliton solutions of a multi-component Gross–Pitaevskii equation for hyperfine spin F =1 spinor Bose–Einstein condensate. The interactions are supposed to be inter-atomic repulsive an...

Sagdeev potential analysis for positively charged dust grains in nonthermal dusty plasma near Mars

The existence of nonlinear dust acoustic (DA) solitary waves for positive dust grains is examined in a dusty plasma (DP). Four charging currents are considered: photoemission, secondary electrons, as well as the electron and ion currents. The nonthermal ion charging current is presented for the first time. Introducing nonthermal ions in the DP system aids in increasing the net positive dust charge, though raising their temperature goes in the opposite direction. There is a maximum value of the ambient plasma potential allowing positive dust charges. The energy equation for the DP system is obtained. The allowed Mach number regime is expanded due to the presence of the nonthermal ions. In the present model, the rarefactive soliton is only permitted. For a constant dust charge, there is a maximum limit of the wave velocity attached to the DA soliton solution. The charging fluctuation always contributes to reducing the amplitude and the width of the produced soliton. The ratio of ion to electron number densities and the nonthermal parameter are two competitors to determine the amplitude and the width of the resultant solitons. Implications of these results to the recorded space phenomena in Martian space and tropical mesosphere are briefly discussed.

Low frequency localized wavepackets in dusty plasmas with opposite charge polarity dust components

The reductive perturbation technique is employed to investigate the modulational instability of dust-acoustic (DA) waves propagating in a four-component dusty plasma. The dusty plasma consists of both positive- and negative-charge dust grains, characterized by a different mass, temperature and density, in addition to a background of Maxwellian electrons and ions. Relying on a multi-fluid plasma model and employing a multiple scales technique, a nonlinear Schrodinger type equation (NLSE) is obtained for the electric potential amplitude perturbation. The occurrence of localized electrostatic wavepackets is shown, in the form of oscillating structures whose modulated envelope is modelled as a soliton (or multi-soliton) solution of the NLSE. The DA wave characteristics, as well as the associated stability thresholds, are studied analytically and numerically. The relevance of these theoretical results with dusty plasmas observed in cosmic and laboratory environments is analysed in detail, by considering realistic multi-component plasma configurations observed in the polar mesosphere, as well as in laboratory experiments.

Construction of Parity-Time Symmetric Potential through the Soliton Theory

A systematic method is presented for the construction of the parity-time (PT) symmetric potentials. The key idea is the transformation between Dirac type and Schrodinger type eigenvalue problems in the inverse scattering method. As a standard example, the modified Korteweg–de Vries (mKdV) equation is considered. There exists a PT symmetric potential corresponding to a soliton solution. One- and two-soliton PT symmetric potentials are given explicitly. The extensions of the theory into other types of solutions and other soliton equations are discussed.

Finite amplitude solitary excitations in rotating magnetized nonthermal complex "dusty… plasmas

The nonlinear dynamics of finite amplitude dust acoustic solitary waves in rotating magnetized nonthermal plasma are investigated. For this purpose, the hydrodynamic equations for the dust grains, nonthermal ion density, and Boltzmann electron distributions together with the Poisson equation are used to derive the energy integral equation with a new Sagdeev potential. It is found that the solitary excitations strongly depend on the nonthermal ion parameters, rotational frequency, as well as dust gyrofrequency. The present investigations may be applicable to the dusty plasma situation near to the moon.

Multicomponent Bright Solitons in F ¼ 2 Spinor Bose-Einstein Condensates

We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirotas direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.

Wave Propagations in the F=1 Spinor Bose–Einstein Condensates

Propagations of nonlinear waves in the quasi-one dimensional F =1 spinor Bose–Einstein condensates are studied. The three-component macroscopic wavefunction obeys a generalized Gross–Pitaevskii equation (nonlinear Schrodinger equation). Plane wave and solitary wave solutions are obtained explicitly. It is shown that the analysis of the plane waves leads to a classification of solitary waves, which are known as polar solitons and ferromagnetic solitons.Propagations of nonlinear waves in the quasi-one dimensional F =1 spinor Bose–Einstein condensates are studied. The three-component macroscopic wavefunction obeys a generalized Gross–Pitaevskii equation (nonlinear Schrodinger equation). Plane wave and solitary wave solutions are obtained explicitly. It is shown that the analysis of the plane waves leads to a classification of solitary waves, which are known as polar solitons and ferromagnetic solitons.

Painleve singularity structure analysis of three component Gross-Pitaevskii type equations

In this paper, we have studied the integrability nature of a system of three-coupled Gross–Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose–Einstein condensates by applying the Painleve singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painleve test.

Matter-Wave Bright Solitons with a Finite Background in Spinor Bose–Einstein Condensates

We investigate dynamical properties of bright solitons with a finite background in the F =1 spinor Bose–Einstein condensate (BEC), based on an integrable spinor model which is equivalent to the mat...

Exact analysis of a δ-function spin-1/2 attractive Fermi gas with arbitrary polarization

The ground state of a one-dimensional δ-function attractive spin-1/2 fermions is studied by the nested Bethe ansatz method. Explicitly, the Gaudin integral equation for the system is solved in the form of power series with arbitrary spin polarization. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. The physical quantities, such as the ground state energy and the chemical potentials, are expressed in terms of the dimensionless coupling constant and the polarization , where c is the coupling constant and are the number densities of the spin-up (down) particles. While in the limiting case P = 1, the system consists of spinless free fermions, the other limit P = 0 describes the BCS–BEC crossover in one dimension. As a function of P, the evolution is continuous and smooth.