Higher order solution of the dust ion acoustic solitons in a warm dusty plasma with vortex-like electron distribution

The ratios of dust to free electron and free to trapped electron temperatures are examined in warm dusty plasmas with vortex-like electron distribution through the derivation of a modified Korteweg–de Vries (MKdV) equation using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the MKdV equation, i.e., the breakdown of the MKdV approximation. To describe the soliton of larger amplitude, the MKdV equation with the fifth-order dispersion term is employed and its higher-order solutions are obtained.     

Solitary waves in dusty plasmas with variable dust charge and two temperature ions

Propagation of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions is analyzed. The Kadomtsev–Petviashivili (KP) equation is derived by using the reductive perturbation theory. A Sagdeev potential for this system has been proposed. This potential is used to study the stability conditions and existence of solitonic solutions. Also, it is shown that a rarefactive soliton can be propagates in most of the cases. The soliton energy has been calculated and a linear dispersion relation has been obtained using the standard normal-modes analysis. The effects of variable dust charge on the amplitude, width and energy of the soliton and its effects on the angular frequency of linear wave are discussed too. It is shown that the amplitude of solitary waves of KP equation diverges at critical values of plasma parameters. Solitonic solutions of modified KP equation with finite amplitude in this situation are derived.     

Multidimensional dust acoustic solitary waves in inhomogeneous magnetized dusty plasmas with nonthermal ions

The linear dispersion relation and a modified variable coefficients Korteweg–de Vries (MKdV) equation governing the three-dimensional dust acoustic solitary waves are obtained in inhomogeneous dusty plasmas comprised of negatively charged dust grains of equal radii, Boltzmann distributed electrons and nonthermally distributed ions. The numerical results show that the inhomogeneity, the nonthermal ions, the external magnetic field and the collision have strong influence on the frequency and the nonlinear properties of dust acoustic solitary waves and both dust acoustic solitary holes (soliton with a density dip) and positive solitons (soliton with a density hump) are excited.     

Quasi-stationary solitons for Langmuir waves in plasmas

The multiple-scale perturbation analysis is used to study the perturbed nonlinear Schrödinger’s equation, that describes the Langmuir waves in plasmas. The perturbation terms include the non-local term due to nonlinear Landau damping. The WKB type ansatz is used to define the phase of the soliton that captures the corrections to the pulse where the standard soliton perturbation theory fails.     

Effects of the dust charge variation and non-thermal ions on multi-dimensional dust acoustic solitary structures in magnetized dusty plasmas

The combined effects of both adiabatic dust charge variation and non-thermally (fast) distributed ions on dust acoustic solitary structures are studied in a magnetized dusty plasmas consisting of the negatively and variably charged hot dust fluid, Boltzmann distributed electrons and non-thermally distributed ions. By using the reductive perturbation method, we derive the Korteweg-de Vries (KdV) equation governing the dust acoustic solitary waves. It is shown that the dust charge variation and the presence of non-thermally distributed ions would modify the nature of dust acoustic solitary structures significantly and may excite both dust acoustic solitary holes (soliton with a density dip) and positive solitons (soliton with a density hump).     

Stochastic perturbation of solitons for Alfven waves in plasmas

The stochastic perturbation of solitons due to Alfven waves in plasmas, is studied in this paper, in addition to the deterministic perturbation terms. The Langevin equations are derived and it is proved that the soliton travels through the plasma with a fixed mean velocity.     

Steady bifurcation and solitons in relativistic laser plasmas interaction

In this paper, steady bifurcation and solitons in relativistic laser plasmas interaction are investigated. At first, a new coupled equation for wake wave and the circularly polarized transversal electromagnetic wave is derived. It is a Hamiltonian system with two degrees of freedom. Then, a steady bifurcation analysis based on the coexistence of three different equilibrium states is given. Finally, a condition for predicting the existence of solitons is obtained in terms of the bifurcation control parameter and Hamiltonian function value. The soliton solutions are found numerically. It is shown that the solitons can exist in appropriate regime of vector potential frequency.     

Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and the kinetic theory of dusty plasmas

We consider the modern state of a consistent kinetic theory of dusty plasmas. We present the derivation of equations for microscopic phase densities of plasma particles and grains. Such equations are suitable for extending the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy to the case of dusty plasmas and for deriving the kinetic equations with regard for both elastic and inelastic particle collisions. Moreover, we describe the effective grain-grain potentials kinetically.     

Theoretic study of dust acoustic waves in a dusty plasma with dust charge variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is investigated by using the formally variable separation approach. New solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma firsthand. We derive exact mathematical expressions and numerical simulation studies for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Dynamics of solitons in plasmas for the complex KdV equation with power law nonlinearity

This paper obtains the 1-soliton solution of the complex KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The soliton perturbation theory for this equation is developed and the soliton cooling is observed for bright solitons. Finally, the dark soliton solution is also obtained for this equation.     

Theoretical results of the dust acoustic waves in a magnetized dusty plasma with different dust particles

In this paper, the nonlinear dust acoustic waves (DAW) in a magnetized dusty plasmas with different dust grains are analytically investigated. New analytical solutions of the governing equation for this system have been obtained for the first time. The exact mathematical expressions of the nonlinear dust waves have been canvassed for the general case in magnetized dusty plasma containing different dust particles.     

Study of the dust acoustic waves in a magnetized dusty plasma with many different dust grains

The nonlinear dust waves in a magnetized dusty plasma with many different dust grains are analytically investigated. New analytical solutions for the governing equation of this system have been obtained for the dust acoustic waves in a dusty plasma for the first time. We derive exact mathematical expressions for the general case of the nonlinear dust waves in magnetized dusty plasma which contains different dust grains.     

The Kadomtsev–Petviashvili (KP), MKP,and coupled KP equations for two-ion-temperature dusty plasmas

It is well known that the Korteweg–de Vires (KdV) equation can describe small but finite amplitude dust acoustic waves in a dusty plasmas. In this paper, we use the reductive perturbation method and derive a Kadomtsev–Petviashvili (KP) equation, a modified KP (MKP) equation and a coupled KP equation for unmagnetized, collisionless, cold, and two-ion-temperature dusty plasmas with N different species of dust grains. We find that if a solitary wave exist in this system, the smaller grains have larger velocities and propagate longer distances than that of larger particles. The comparisons are given between the dusty plasma composed by different dust particles and the mono-sized dusty plasma.     

Semi-analytical study of variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive ion velocity distribution

An attempt is made to study variable charge dust acoustic (DA) solitons within the theoretical framework of the Tsallis statistical mechanics. The correct nonextensive ion charging current is presented for the first time based on the orbit motion limited (OML) approach. The variable dust charge is then expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate nonlinear localized DA waves in a charge varying dusty plasma with nonextensive ions more rigorously. Our results reveal that the ion nonextensivity makes the dust acoustic solitary structure more spiky. As the ions deviate from their thermodynamic equilibrium, the dust grain charge becomes least negative and the dust accumulation more effective. In addition, the nonextensive character of the ions contributes to the electron depletion. The latter is more pronounced as the ions evolve far away from their thermal equilibrium. Our results should help in providing a good fit between theoretical and experimental results.     

Stability criterion for solitons

Institute of Chemical Physics, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 1, pp. 28–33, January, 1990.     

Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas

Plasmas are believed to be possibly the most abundant form of ordinary matter in the Universe, supporting a variety of the wave phenomena, while a dusty plasma is of interest as a non-Hamiltonian system of interacting particles. In this Letter, symbolic computation on an observationally/experimentally-supported (2+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation is done, for certain dust-acoustic, electron-acoustic, positron-acoustic, magneto-acoustic, dust-magneto-acoustic, ion-acoustic, dust-ion-acoustic and/or quantum-dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. Auto-Bäcklund transformation and families of the solitonic solutions are obtained, for the electrostatic wave potential, perturbation of the magnitude of the magnetic field, fluctuation of electron or ion density, or radial-direction component of the velocity of ions or dust particles, relying on such plasma coefficient functions as the nonlinearity, dispersion, dusty-fluid-viscosity/Burgers-dissipation, geometric-effect and diffraction/transverse-perturbation coefficients. Shock structures presented in this Letter are very close to the experimental results previously reported. Future plasma observations/experiments might verify some other effects offered by our analytic results with respect to those plasma coefficient functions.     

A theoretical description for solitons in polyacetylene

The bond-alternation domain walls or the solitons in the dimerized polyacetylene are analyzed theoretically. The width of the soliton is many times the period of the chain, so that the soliton can be reasonably well described by a continuum model. Because of the existence of the bond-alternation domain walls, the electron density is different definitely. Thus the electron density can be used to describe the formation of the domain walls, and a self-trapped potential is discussed and introduced in the Hamiltonian. It is shown that the envelope of the wave functions of the chain is governed by the nonlinear Schr?dinger equation which has soliton solutions. Then the shape of the soliton is determined analytically which is in accordance with the numerical calculations by Su, Schrieffer and Heeger. This implies that the bond-alternation domain wall or the soliton is observed as the envelope of the wave function.     

A stochastic model for solitons

The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg‐like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514–3519]. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Solitary waves in self-gravitating dusty plasma

The electrostatic dust acoustic wave is studied in a uniform gravitating dusty plasma, when the self-gravitation does alter the linear modes given by the dispersion relation. It is observed that instead of a single nonlinear equation we get two coupled KdV-like systems. It is observed that such a system can sustain solitary-wave-like excitations under suitable conditions on the plasma parameters. Such an analysis is very important in ascertaining the fate of a grain orbiting around a magnetized planet in space, where there is a competition between magnetic and gravitational forces. And this in turn gives rise to the question of magnetogravitational instability, which plays an important role in star formation. It is observed that the gravitational soliton's amplitude, being proportional to the Jeans frequency, is always smaller compared to the electrostatic counterpart.