Table of contents

We extend the Malfliet method of obtaining multisoliton solutions of the Korteweg–de Vries equation to construct several classes of multicnoidal and multitravelling wave solutions for a variety of nonlinear equations of mathematical physics. We illustrate the procedures for single nonlinear equations as well as for coupled nonlinear systems. Several classes of multicnoidal wave solutions are obtained for the considered model equations. Also, multitravelling wave solutions are constructed as reduced cases from the constructed multicnoidal wave solutions. Finally, we conclude the paper and give some features and comments.

Assume that a system of ordinary differential equations can be written in the Lax representation. We show that the Kronecker product can be used to construct new Lax representations. The time-evolution is also given.

The wave equation has in free space many classes of localized solutions with finite energy propagating without distortion which would make these pulses useful in many domains as soon as one is able to launch them. Among these localized waves, the so-called focus wave modes are the most serious candidates and could be constituents of the cosmic gamma rays recently observed. So the analysis of their propagation in nonhomogeneous media, a problem of interest in itself, could be used to deal with their behavior in the interstellar space. We assume here a medium with a refractive index varying slightly with the altitude, a bit like in troposphere. We get approximate expressions for plane waves and focus wave modes propagating in this medium.

Using the NU method [A F Nikiforov and V B Uvarov 1988 "Special Functions of Mathematical Physics" (Birkhauser, Basel)], we investigated the real eigenvalues of the complex and/or PT-symmetric, non-Hermitian and the exponential type systems, such as Pöschl–Teller and Morse potentials.

Optogalvanic laser spectroscopy has been applied to measure the hyperfine structure of 12 spectral lines of Mn I in the wavelength regions of 660–645 nm and 933–911 nm. Experimental hyperfine structure constants A and B of the isotope ⁵⁵Mn have been determined for seven levels of even and seven levels of odd parity. Additionally, a parametric analysis of the fine structure and the magnetic dipole hyperfine structure has been performed for the three even configurations 3d⁵4s², 3d⁶4s and 3d⁷. Very large values for the ratio a_3d¹⁰/a_3d⁰¹ are found. Theoretical predictions for the magnetic dipole hyperfine structure constants A for all levels of the configurations 3d⁵4s², 3d⁶4s and 3d⁷ are given.

The radiation of a wall-stabilized arc (operating in argon with small admixtures of CO₂) was studied to determine relative transition probabilities for components of some infrared multiplets of neutral carbon and oxygen (wavelengths between 800 and 1500 nm). The absolute transition probabilities were obtained by normalisation of relative values received for carbon and oxygen lines: C I λ = 940.573 nm, A_ki = 2.9 · 10⁷ s^-1; O I λ = 844.65 nm, A_ki = 3.2 · 10⁷ s^-1 as standards taken from literature. An arc current of 35 A allows the diagnostic of this plasma under assumption of local thermodynamic equilibrium (LTE) in the created plasma. The A_ki-values obtained are compared to available experimental and theoretical data.

Transition energies, oscillator strengths and lifetimes of the excited states for boron-like ions, Ne⁺⁵, Na⁺⁶ and Mg⁺⁷, have been calculated using multireference relativistic configuration interaction method based on the no-pair Dirac–Coulomb–Breit Hamiltonian. Analytic basis sets of Gaussian-type functions are employed to expand the upper and lower components of the Dirac four-spinors in the matrix Dirac–Fock self-consistent field and relativistic MR CI procedures. Transition energies are compared with experiment and other results.

We report on calculation of electron-impact excitation cross sections for Li-like ions of boron and beryllium. The data were produced with a number of modern methods in atomic collision theory, such as convergent close-coupling, K-matrix and Coulomb–Born-exchange. The results obtained are compared with other calculations and available expermental data, and the recommended cross sections for all transitions between atomic terms with principal quantum numbers n ≤ 4 are presented as tables of fitting parameters.

Intervalence band dynamics of free holes in infrared fields is studied. A realistic valence band structure is used to simulate simultaneous excitation of split-off, heavy- and light-mass bands by femtosecond duration pulses. The decoherence due to phonon and ionized impurity scattering is taken into account in a quantum-mechanical density matrix. The excitation patterns in the Brillouin zone and hole distribution dynamics are presented. It is shown that it is possible to obtain high excitation levels in the valence band and dynamical inversion even in presence of dissipation, if femtosecond pulses are properly tailored.

Linear and weakly nonlinear stabilities of two-layer flows between two concentric circular cylinders are investigated. Two different dielectric inviscid fluids are assumed to flow with different velocities in the two separate layers, whose interface is cylindrical. Hence the flow field is assumed to be axi-symmetric. The two fluids are influenced by a radial electric field due to surface charges at the interface. The critical magnitude of the electric field is obtained as a function of the velocity difference in the linear stability analysis. Based on the multiple scales technique, two nonlinear Schrödinger and Klein-Gordon equations are derived. The modulation instability of a finite wavetrain solution is discussed and compared with the linear instability condition. The analytical results are numerically confirmed, hence stability diagrams are obtained for different sets of physical parameters. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.

The foreign-gas broadening parameter for fluoroform molecules interacting with nonpolar BCl₃ molecule as perturber has been measured and the collision cross section has been determined. The results are pressure broadening coefficient C_w = (43 ± 1) [kHz/Pa] for J = 1 ← 0 rotational transition of CHF₃ molecule in mixture with BCl₃ gas, and collision cross section σ_exp = 294.0 [Ų]. Experimental linewidth parameter is interpreted using Anderson–Tsao–Curnutte as well as Murphy–Boggs theories for the mixed- interaction case. From this analysis a value of molecular quadrupole moment Q = (4.1 ± 0.2) [DŲ] of boron trichloride molecule has been obtained.

Angular dependence of the collective plasma screening and quantum effects on the elastic electron–ion scattering cross section are investigated in strongly coupled semiclassical plasmas. The effective screened pseudopotential taking into account both the screening and quantum effects is applied to describe the electron–ion interactions in semiclassical plasmas. The Born approximation is considered to obtain the electron–ion scattering amplitude and differential cross section including the quantum and collective effects. The results show that the collective and quantum effects significantly reduce the differential electron–ion scattering cross sections, especially, for backward scattering directions. The quantum screening effects on the differential scattering cross section are found to be small for forward scattering. It is also found that the quantum mechanical effects are more significant than the collective plasma screening effects in strongly coupled semiclassical plasmas.

Properties of three-dimensional wake potentials around a stationary dust particulate in a plasma with magnetic field-aligned ion flows have been theoretically studied. Numerical and analytical results reveal that the wakefield periodicity along the magnetic field direction is significantly affected (unaffected) for a stronger (weaker) magnetic field, while the periodicity in the perpendicular plane is unaffected for both high-and low-density plasmas.

The long-wave low-frequency electromagnetic excitations in a colloidal plasma with a dynamic recharging are investigated. In the weakly nonlinear regime, stationary spectra of thermal fluctuations are obtained. It is shown that in this case, the dynamic recharging makes a substantial contribution to the renormalized viscosity coefficient and gives rise to renormalized absorption frequency. For strong dynamic recharging, the anomalous diffusion is essentially decreased (with no Bohm-like behaviour) which may be of interest for the fusion problem.

The interactions between an ultra-short ultra-intense laser pulse and a solid target with and without a low density pre-plasma are examined. The electrons in the pre-plasma can be trapped and accelerated by the ponderomotive force of a propagating laser pulse, and escape from the pulse as the latter reflects from the target surface, preserving high energy. While in laser interaction with a target without pre-plasma, the maximum energy achieved is much lower. In this sense, the pre-plasma is advantageous for energetic electron generation in the ultra-short ultra-intense laser–solid interaction.

The photon induced K x-ray fluorescence cross-sections (σ_Kα, σ_Kβ) for Co, Ni and Cu in F and Cl compounds were investigated. Measurements were carried out at ten different energies in the interval 8.14–16.89 keV by using secondary excitation method. K x-rays emitted by samples were counted by a Si(Li) detector with resolution 160 eV at 5.9 keV. It is observed that K x-ray fluorescence cross-sections (σ_Kα, σ_Kβ) for Co, Ni and Cu in F and Cl compounds decrease with increasing excitation energy. Particularly, K x-ray fluorescence cross-sections (σ_Kα, σ_Kβ) for F compounds of this element are higher than the theoretical values and those of Cl compounds of this element. Obtained values were compared with theoretical values of pure elements.

This paper reports the results of a scattering study on aqueous solutions of Poly(Ethylene Oxide), PEO, with Molecular Weight M_w 600000 performed by means of Small Angle Neutron Scattering, SANS, and Photon Correlation Spectroscopy, PCS. The results obtained by the integrated application of these techniques indicate a swollen state of the polymer, i.e. that in the investigated temperature range water behaves as a good solvent for PEO with no evidence of aggregation. It clearly emerges that the unaggregate state provides the starting reference point for clarifying many of the friction properties of such system.

The influence of electron drift velocity shear on the Farley–Buneman instability in the ionospheric E-region is considered. First, we consider evolution with time of small-amplitude Farley–Buneman waves in the sheared plasma using Laplace transform in time and the exact solution for the model linear layer. As a result we obtain the Farley–Buneman waves with the component of the wave vector along the non-uniformity increasing with time. Second, we consider development of the Farley–Buneman instability in the sheared plasma using an approximate analytical method. We find that the electron drift velocity shear has a stabilizing influence on the Farley–Buneman instability. Also we find that the Farley–Buneman waves with the maximum amplitude have phase velocities close to the ion-acoustic velocity.