Effects of positron density and temperature on ion acoustic dressed solitons in an electron–positron–ion plasma

Ion acoustic dressed solitons in a three component plasma consisting of cold ions, hot electrons and positrons are studied. Using reductive perturbation method, Korteweg–de Vries (KdV) equation and a linear inhomogeneous equation, governing respectively the evolution of first and second order potentials are derived for the system. Renormalization procedure of Kodama and Taniuti is used to obtain nonsecular solutions of these coupled equations. It is found that electron–positron–ion plasma system supports only compressive solitons. For a given amplitude of soliton on increasing the positron concentration, velocity of the KdV as well as dressed soliton increases. For any arbitrary values of soliton's amplitude and positron concentration, velocity of the dressed soliton is found to be larger than that of the KdV soliton. For small amplitude of solitons, the width of KdV as well as dressed soliton decreases as positron concentration increases and width of dressed soliton is found to be larger than that of the KdV soliton. However, for a large value of soliton's amplitude as concentration of positrons increases, instead of decreasing width of dressed soliton starts to increase.     

Stationary solitons of the fifth order KdV-type. Equations and their stabilization

Exact stationary soliton solutions of the fifth order KdV type equation, u_t + αu^pu_x + βu_3x + γu_5x = 0, are obtained for any p (> 0) in case αβ > 0, Dβ > 0, βγ < 0 (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case p ≥ 5. Various properties of these solutions are discussed. In particular, it is shown that for any p these solitons are lower and narrower than the corresponding γ = 0 solitons. Finally, for p = 2 we obtain an exact stationary soliton solution even when D, α, β, γ are all > 0 and discuss its various properties.     

Oblique Interaction of Ion-Acoustic Solitary Waves in e-p-i Plasmas

In this study, we investigate the oblique collision of two ion-acoustic waves (IAWs) in a three-species plasma composed of electrons, positrons, and ions. We use the extended Poincare-Lighthill-Kuo (PLK) method to derive the two-sided Korteweg-de-Vries (KdV) equations and Hirota’s method for soliton solutions. The effects of the ratio (δ) of electron temperature to positron temperature and the ratio (p) of the number density of positrons to that of electrons on the phase shift are studied. It is observed that the phase shift is significantly influenced by the parameters mentioned above. It is also observed that for some time interval during oblique collision, one practically motionless composite structure is formed, i.e., when two ion-acoustic waves with the same amplitude interact obliquely, a new non-linear wave is formed during their collision, which means that ahead of the colliding ion-acoustic solitary waves, both the amplitude and width are greater that those of the colliding solitary waves. As a result, the nonlinear wave formed after collision is a new one and is delayed. The oblique collision of solitary waves in a two-dimensional geometry is more realistic in high-energy astrophysical pair plasmas such as the magnetosphere of neutron stars and black holes.     

Drift ion acoustic solitons in an inhomogeneous 2-D quantum magnetoplasma

Linear and nonlinear propagation characteristics of quantum drift ion acoustic waves are investigated in an inhomogeneous two-dimensional plasma employing the quantum hydrodynamic (QHD) model. In this regard, the dispersion relation of the drift ion acoustic waves is derived and limiting cases are discussed. In order to study the drift ion acoustic solitons, nonlinear quantum Kadomstev-Petviashvilli (KP) equation in an inhomogeneous quantum plasma is derived using the drift approximation. The solution of quantum KP equation using the tangent hyperbolic (tanh) method is also presented. The variation of the soliton with the quantum Bohm potential, the ratio of drift to soliton velocity in the co-moving frame, , and the increasing magnetic field are also investigated. It is found that the increasing number density decreases the amplitude of the soliton. It is also shown that the fast drift soliton (i.e., v_*>u) decreases whereas the slow drift soliton (i.e., v_*<u) increases the amplitude of the soliton. Finally, it is shown that the increasing magnetic field increases the amplitude of the quantum drift ion acoustic soliton. The stability of the quantum KP equation is also investigated. The relevance of the present investigation in dense astrophysical environments is also pointed out.     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Solutions of a Particle with Fractional <Emphasis Type="Italic">δ</Emphasis>-Potential in a Fractional Dimensional Space

A Fourier transformation in a fractional dimensional space of order λ (0<λ≤1) is defined to solve the Schrödinger equation with Riesz fractional derivatives of order α. This new method is applied for a particle in a fractional δ-potential well defined by V(x)=?γ δ ^λ (x), where γ>0  and δ ^λ (x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0<λ<α. The results for λ=1 and α=2 are in exact agreement with those presented in the standard quantum mechanics.     

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.     

Overall width,mean peak width and the uncertainty principle

We define the overall width W and the mean peak width w of a normalized function ψ (x). We show W ≤ 2Δx and w > (2Δp)^?1, where Δx and Δp are standard deviations. Analogous relations hold for the Fourier transform. The uncertainty principle is expressed precisely by these relations, not by $\text{ΔxΔp ≥}\text{1}\text{2}$.     

Low frequency electrostatic nonlinear structures in an inhomogeneous magnetized non-Maxwellian electron–positron–ion plasma

The properties of low frequency (coupled acoustic and drift wave) nonlinear structures including solitary waves and double layers in an inhomogeneous magnetized electron–positron–ion (EPI) nonthermal plasma with density and temperature inhomogeneities are studied in a simplified way. The nonlinear differential equation derived here for the study of double layers in the inhomogeneous EPI plasma resembles with the modified KdV equation in the stationary frame. But the method used for the derivation of nonlinear differential equation is simple and consistent to give both the stationary solitary waves and double layers. Further, the illustrations show that superthermality κ, drift velocity and temperature inhomogeneity have significant effects on the amplitude, width, and existence range of the structures.     

Soliton solutions of some nonlinear evolution equations with time-dependent coefficients

In this paper, we obtain exact soliton solutions of the modified KdV equation, inhomogeneous nonlinear Schrödinger equation and G(m, n) equation with variable-coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.     

Bright and dark soliton solutions for some nonlinear fractional differential equations

In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney(m BBM) equation, the time fractional m Kd V equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense.     

Thermal expansion and kinetic coefficients of crystals

Electrical (ρ) and thermal (W) resistivities and thermal expansion coefficient (β) of Cu, Zn, Al, Pb, Ni, β-brass, Al₂O₃, NaCl, Si, SiO₂(∥), and SiO₂(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature (T_D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5-4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ^ph/ρ^*≡βT and W^ph/W^*≡βT (where ρ^ph is the phonon electrical resistivity, is the characteristic electrical resistivity, W^ph is the phonon thermal resistivity, and W^*=k_BG/qc_p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.     

Evidence of the Non-Strange Partner of Pentaquark from the Elementary K +Λ Photoproduction

The existence of the J ^p  = 1/2⁺ narrow resonance predicted by the chiral soliton model has been investigated by utilizing the new kaon photoproduction data. For this purpose, we have constructed two phenomenological models, which are able to describe kaon photoproduction from threshold up to W = 1,730 MeV. By varying the resonance mass, width, and KΛ branching ratio in this energy range we found that the most convincing mass of this resonance is 1,650 MeV. Using this result we estimate the masses of other antidecuplet family members.     

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Effects of plasma nonextensivity on the nonlinear cnoidal ion‐acoustic wave in unmagnetized electron‐positron‐ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion‐acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron (σ). For all of the acceptable values of q, the cnoidal ion‐acoustic wave is compressive. Results show that ion‐acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and σ on the characteristics of the ion‐acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency.     

A discrete KdV equation hierarchy: continuous limit,diverse exact solutions and their asymptotic state analysis

In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.     

Density and well width dependences of the effective mass of two-dimensional holes in (100) GaAs quantum wells measured using cyclotron resonance at microwave frequencies

Cyclotron resonance at microwave frequencies is used to measure the band mass (m_b) of the two-dimensional holes (2DHs) in carbon-doped (100) GaAs/ Al_xGa_1−xAs heterostructures. The measured m_b shows strong dependences on both the 2DH density (p) and the GaAs quantum well width (W). For a fixed W, in the density range (0.4×10¹¹ to 1.1×10¹¹ cm⁻²) studied here, m_b increases with p, consistently with previous studies of the 2DHs on the (311)A surface. For a fixed , m_b increases from 0.22m_e at to 0.50m_e at , and saturates around 0.51m_e for .     

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional （2D） KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach.     

Transverse momentum of hadrons produced in ν and ν interactions on an isoscalar target in BEBC

The average transverse momentum squared, 〈p_⊥²〉, of hadrons is studied as a function of W² and of Q² for ν and $\text{ν}$ interactions on an isoscalar target. An increase of 〈p_⊥²〉 with W² is observed for the hadrons emitted forward in the hadronic c.m.s. The p_⊥ dependence of the fragmentation function is found to factorise from the structure function at fixed W, but does not factorise at fixed Q². Unlike the case of forward-going particles, the 〈p_⊥²〉 of hadrons going backward in the c.m.s. shows no strong dependence on W².     

KdV Equation with Self-consistent Sources in Non-uniform Media

Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.