Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas

Traveling wave solution of the Gardner equation is studied analytically by using the two dependent (G^′/G,1/G)-expansion and (1/G^′)-expansion methods and direct integration. The exact solutions of the Gardner equations are obtained. Our analytic solutions are applied to the unmagnetized four-component and dusty plasma systems consisting of hot protons and electrons to investigate dynamical features of the solitons and shock waves produced in these systems. A wide variety of parameters of the plasma is used, and the basic features of the Gardner solitons that are beyond the existing study in literature are found. It is observed that the analytic solutions from (G^′/G,1/G)-expansion and (1/G^′)-expansion methods only produce shock waves but the solitary waves are found from the analytic solutions derived from the direct integration. It is also noted that the superhot electrons and relative mass density of the electrons significantly effect the soliton’s amplitude, width, and position. We have also numerically proved that the combination of every value of nomalized density μ₁ or temperature ratio σ₁ with the other sets of plasma parameters creates a region where the solutions have similar physical properties. The time-dependent behavior of the soliton is also studied, and a periodic motion of soliton along the phase variable η is found during the evolution. The investigations and the limits presented in this study may be helpful for studying and understanding the nonlinear properties of the solitary and shock waves seen in various physical and astrophysical plasma systems.     

Exciton and intracenter radiative recombination in ZnMnTe and CdMnTe quantum wells with optically active manganese ions

The emission spectra of Zn_1?x Mn _x Te/Zn_0.6Mg_0.4Te and Cd_1?x Mn _x Te/Cd_0.5Mg_0.5Te quantum-well structures with different manganese concentrations and quantum-well widths are studied at excitation power densities ranging from 10⁵ to 10⁷ W cm^?2. Under strong optical pumping, intracenter luminescence of Mn²⁺ ions degrades as a result of the interaction of excited managanese ions with high-density excitons. This process is accompanied by a strong broadening of the emission band of quantum-well excitons due to the exciton-exciton interaction and saturation of the exciton ground state. Under pumping at a power density of 10⁵ W cm^?2, stimulated emission of quantum-well excitons arises in CdTe/Cd_0.5Mg_0.5Te. The luminescence kinetics of the quantum-well and barrier excitons is investigated with a high temporal resolution. The effect of the quantum-well width and the managanese concentration on the kinetics and band shape of the Mn²⁺ intracenter luminescence characterized by the contribution of the manganese interface ions is determined.     

Excitons in monoclinic zinc diphosphide: The <Emphasis Type="Italic">A</Emphasis>-exciton series and Fano effect

The A-exciton series in the absorption spectra of β-ZnP₂ monoclinic zinc diphosphide samples is investigated at different directions of the wave vector and different polarization states of radiation. It is shown that the oscillator strengths determined for the observed transitions are adequately described by the relationship F _n ∝n^?3 characteristic of S-type exciton states. The assumption is made that the A-exciton series is associated with the partially allowed dipole transitions to nS states of the orthoexciton with Γ ₂ ^? (x) symmetry at m _s =0. These states are mixed, to a first approximation, with nS states of the Γ ₂ ^? (z) singlet exciton due to the spin-orbit 2 interaction and are split off by the long-range (nonanalytical) part of the exchange interaction. The Fano antiresonances arise in the absorption spectra at resonances of the A-exciton series when the radiation vector E (or the induction vector D) has a component along the crystallographic axis c. These antiresonances are induced by the configurational interaction of discrete exciton states of the A series with the continuum of the exciton-phonon spectrum due to indirect transitions to the 1S band of the singlet exciton with phonon emission.     

Freezing of Energy of a Soliton in an External Potential

In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential ?V of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer r, the energy of such a mechanical system is almost conserved up to times of order ?^?r. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order ?^?r.     

Effect of correlation between the shallow and deep metastable level subsystems on the excitonic photoluminescence spectra in <Emphasis Type="Italic">n</Emphasis>-GaAs

The excitonic photoluminescence spectra of GaAs epitaxial layers are studied. Changes in the relative arrangement of shallow and deep centers in the tetrahedral lattice are shown to bring about changes in the decay kinetics and the shape of the (D⁰, x) emission line (corresponding to an exciton bound to a shallow neutral donor). This change in the excitonic photoluminescence spectra is caused by dispersion in the exciton binding energy of shallow donors E_D, the dispersion being a result of the influence of the subsystem of deep metastable defects in n-GaAs crystals.     

Scattering of an exciton polariton by impurity centers in GaAs

Scattering of an exciton polariton by impurity centers at low temperatures has not been investigated comprehensively in spite of its significant role in processes accompanying Bose–Einstein condensation of an exciton polariton. For studying the peculiarities of the interaction of an exciton polariton with impurity centers, we have studied the integrated absorption of the ground state (n ₀ = 1) of the exciton in GaAs in thin (micrometer-thick) wafers with an appreciable optical transmission. Comparative analysis of the transmission in the vicinity of the exciton resonance performed on 15 samples of crystalline GaAs wafers with different concentrations N of impurity has revealed an unexpected regularity. The value of N increases by almost five decimal orders of magnitude, while the normalized spectrally integrated absorption of light exhibits a slight increase, following the power dependence N ^m on the concentration, where m = 1/6. It has been shown that this dependence indicates the diffusion mechanism of propagation of the exciton polaritons through the bulk of the semiconductor, which is present along with the ballistic propagation of light through the sample.     

Landau-Level Quantization of the Yellow Excitons in Cuprous Oxide

Lately, the yellow series of P-excitons in cuprous oxide could be resolved up to the principal quantum number n = 25. Adding a magnetic field, leads to additional confinement normal to the field. Thereby, the transition associated with the exciton n is transformed into the transition between the electron and hole Landau levels with quantum number n, once the associated magnetic length becomes smaller than the related exciton Bohr radius. The magnetic field of this transition scales roughly as n^–3. As a consequence of the extended exciton series, we are able to observe Landau level transitions with unprecedented high quantum numbers of more than 75.     

Soliton dynamics in a spin nematic

One-dimensional localized waves, which can be considered as soliton elementary excitations, exist in a magnet with a unit spin and comparable bilinear and biquadratic spin-spin interactions, with which the state of spin nematic is realized. These excitations are characterized by a certain momentum P and a certain energy E. The structure of these solitons has been found, and the E = E(P) dependence, which plays the role of the dispersion law of these soliton elementary excitations, has been constructed. The energy of a soliton with a certain momentum is shown to be lower than that of the quasiparticles of a linear theory. At small momenta, these E = E(P) dependences of the soliton and quasiparticles coincide asymptotically. The dependence of the soliton energy on the soliton momentum is a periodic function with a period P ₀ = π?/a, whose value does not depend on exchange integrals and depends only on a single crystal parameter, namely, the interatomic distance a. These soliton excitations have common features with the so-called Lieb states, which are well known in many condensed matter models.     

Antiferroelectric films of deuterated betaine phosphate

Thin films of partially deuterated betaine phosphate have been grown by the evaporation on Al₂O₃(110) and NdGaO₃(001) substrates with a preliminarily deposited structure of interdigitated electrodes. The grown films have a polycrystalline block structure with characteristic dimensions of blocks of the order of 0.1–1.5 mm. The degree of deuteration of the films D varies in the range of 20–50%. It has been found that, at the antiferroelectric phase transition temperature T_c^afe = 100–114 K, the fabricated structures exhibit an anomaly of the electrical capacitance C, which is not accompanied by a change in the dielectric loss tangent tanδ. The strong-signal dielectric response is characterized by the appearance of a ferroelectric nonlinearity at temperatures T >T_c^afe, which is transformed into an antiferroelectric nonlinearity at T <T_c^afe. With a further decrease in the temperature, double dielectric hysteresis loops appear in the antiferroelectric phase. The dielectric properties of the films have been described within the framework of the Landau-type thermodynamic model taking into account the biquadratic coupling ξP²η² between the polar order parameter P and the nonpolar order parameter η with a positive coefficient ξ. The E–T phase diagram has been constructed.     

Propagation and interaction of solitons for nonintegrable equations

We describe an approach to the construction of multi-soliton asymptotic solutions for nonintegrable equations. The general idea is realized in the case of N waves, N = 1, 2, 3, and for the KdV-type equation with nonlinearity u ⁴. A brief review of asymptotic methods as well as results of numerical simulation are included.     

On wave and rheidity properties of the Earth’s crust

The properties of the Earth’s solid crust have been studied on the assumption that this crust has a block structure. According to the rotation model, the motion of such a medium (geomedium) follows the angular momentum conservation law and can be described in the scope of the classical elasticity theory with a symmetric stress tensor. A geomedium motion is characterized by two types of rotation waves with shortand long-range actions. The first type includes slow solitons with velocities of 0 ≤ V_sol ≤ c0, max = 1–10 cm s^–1; the second type, fast excitons with V₀ ≤ V_ex ≤ V_S–V_P. The exciton minimal velocity (V₀ = 0) depends on the energy of the collective excitation of all seismically active belt blocks proportional to the Earth’s pole vibration frequency (the Chandler vibration frequency). The exciton maximal velocity depends on the velocities of S (V_S ≈ 4 km s^–1) and/or P (V_P ≈ 8 km s^–1) seismic (acoustic) waves. According to the rotation model, a geomedium is characterized by the property physically close to the corpuscular–wave interaction between blocks that compose this medium. The possible collective wave motion of geomedium blocks can be responsible for the geomedium rheidity property, i.e., a superplastic volume flow. A superplastic motion of a quantum fluid can be the physical analog of the geomedium rheid motion.     

Computational studies of third-order nonlinear optical properties of pyridine derivative 2-aminopyridinium p-toluenesulphonate crystal

In this note, method of Lie symmetries is applied to investigate symmetry properties of time-fractional K(m, n) equation with the Riemann–Liouville derivatives. Reduction of time-fractional K(m, n) equation is done by virtue of the Erdélyi–Kober fractional derivative which depends on a parameter α. Then soliton solutions are extracted by means of a transformation.     

Kinetics of pulsed cathodoluminescence

The kinetics of pulsed cathodoluminescence, which appears upon irradiation of condensed media with high-power electron beams of nanosecond duration, is analyzed. Four types of emission are considered: recombination emission, exciton emission, intracenter emission, and emission of electron and hole centers. It is found that the maximum difference in the kinetics of the intensities of emission of these types occurs in the time interval t≤t ₁≈A ^?1, and, in the far afterglow, an exponential decay occurs with the characteristic time (2A)^?1 for the first and second types of luminescence and A ^?1 for the fourth type. For the intracenter luminescence, the decay time is equal to (2A)^?1 and A _i ^?1 for short-lived and long-lived radiative levels, respectively (A and A _i are the probabilities of linear recombination of electron-hole pairs and decay of a radiative level, respectively). In the case of long-lived radiative levels, a strong peak is observed in the spectrum of intracenter luminescence in the far afterglow.     

Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

Galvanomagnetic study of the quantum-well valence band of germanium in the Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript>/Ge/Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript> potential well

The structure of the quantum-well valence band in a Ge(111) two-dimensional layer is calculated by the self-consistent method. It is shown that the effective mass characterizing the motion of holes along the germanium layer is almost one order of magnitude smaller than the mass for the motion of heavy holes along the [111] direction in a bulk material (this mass is responsible for the formation of quantum-well levels). This creates a unique situation in which a large number of subbands appear to be populated at moderate values of the layer thickness d _w and the hole concentration p _s . The depopulation of two or more upper subbands in a 38-nm-thick germanium layer at a hole concentration p _s = 5 × 10¹⁵ m^?2 is revealed from the results of measuring the magnetoresistance in a strong magnetic field aligned parallel to the germanium layers. The destruction of the quantum Hall state at a filling factor ν = 1 indicates that the two lower subbands merge together in a self-formed potential profile of the double quantum well. It is demonstrated that, in a quasi-two-dimensional hole gas, the latter effect should be sensitive to the layer strain.     

Description of cross sections for photonuclear reactions in the energy range between 7 and 140 MeV

A combination of the exciton and evaporation models is used to describe photonuclear reactions induced in light, medium-mass, and heavy nuclei by photons of energy in the range 7 ≤ E _γ ≤ 140 MeV. Two mechanisms of the photoexcitation of nuclei are considered. These are the formation of a giant dipole resonance at energies in the range E _γ ? 30 MeV and quasideuteron photoabsorption, which is dominant at energies in the region E _γ ? 40 MeV. The density of particle-hole states, which appears in the exciton model, is calculated on the basis of the Fermi gas model. The emission of two preequilibrium particles is taken into account in describing the quasideuteron reaction channel. The effect of isospin conservation on giant-dipole-resonance decay accompanied by photonucleon emission is examined. The model in question is used to describe cross sections for photon-induced reactions on ²⁶Mg, ⁵⁴Fe, ^{112,118,119,124}Sn, and ¹⁸¹Ta nuclei.     

Spectroscopy of resonant excitation of exciton luminescence of GaSe–GaTe solid solutions

The luminescence excitation spectra of localized excitons in GaSe_0.85Te_0.15 solid solutions have been investigated at the temperature T = 2 K. It has been shown that the excitation spectra of excitons with the localization energy ε > 10 mV exhibit an additional maximum M _E located on the low-energy side of the maximum corresponding to the free exciton absorption band with n = 1. It has been found that the shift in the position of the maximum M _E in the excitation spectrum with respect to the energy of detected photons increases as the energy of detected photons decreases, i.e., with an increase in the localization energy of excitons. Under the resonant excitation of localized excitons by a monochromatic light from the region of the exciton emission band, in the exciton luminescence spectrum on the low-energy side from the excitation line, there is also a maximum of the luminescence (M _L ). The energy distance between the position of the excitation line and the position of the maximum in the luminescence spectrum increases with a decrease in the frequency of the excitation light. The possible mechanisms of the formation of the described structure of the luminescence excitation and exciton luminescence spectra of GaSe_0.85Te_0.15 have been considered. It has been concluded that the maximum M _E in the excitation spectrum and the maximum M _L in the luminescence spectrum are attributed to electronic–vibrational transitions with the creation and annihilation of localized excitons, respectively.     

<Superscript>14</Superscript>N Nuclear Magnetic Resonance and Relaxation in the Paramagnetic Region of Uranium Mononitride

The spin susceptibility of a polycrystalline sample of uranium mononitride UN is studied by measuring the ¹⁴N NMR line shift, spin–lattice relaxation rates of the nuclear spin, and static magnetic susceptibility in the temperature region of 1.5T_N < T < 7T_N A joint analysis of the results obtained has revealed the temperature dependence of the characteristic energy of spin fluctuations of the uranium 5f electrons: Γ_nmr(T) ∝ T^0.54(4) close to the dependence Γ(T) ∝ T^0.5 characteristic of concentrated Kondo systems above the coherent state formation temperature.     

Codimension One Threshold Manifold for the Critical gKdV Equation

We construct the “threshold manifold” near the soliton for the mass critical gKdV equation, completing results obtained in Martel et al. (Acta Math 212:59–140, 2014, J Math Eur Soc 2015). In a neighborhood of the soliton, this C¹ manifold of codimension one separates solutions blowing up in finite time and solutions in the “exit regime”. On the manifold, solutions are global in time and converge locally to a soliton. In particular, the soliton behavior is strongly unstable by blowup.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.