Table of contents

Considering the inhomogeneities of media, a generalized Kadomtsev–Petviashvili equation with time-dependent coefficients is hereby investigated with the aid of symbolic computation. The exact analytic one- and two-soliton solutions under certain constraints are obtained by employing the variable-coefficient balancing-act method and Hirota method. Based on its bilinear form, the Lax pair, auto-Bäcklund transformation (in both the bilinear form and the Lax pair form) and nonlinear superposition formula for such an equation are presented. Moreover, some figures are plotted to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

In this work, the effect of the screening due to plasma surrounding in the atomic magnitudes of non-hydrogenic ions immersed in strongly coupled plasmas is analysed. The atomic magnitudes are evaluated in the relativistic detailed configuration accounting approach making use of a central analytical potential developed to model many-electron ions, which includes plasma effects following the ion-sphere (IS) model. In particular, the potential proposed, the energy levels, the total energy and the oscillator strengths are studied. The analysis is made in terms of the plasma average ionization degree, IS radius, plasma coupling parameter and ion stage. Comparisons with other results available in the literature are made in order to check our conclusions.

The exact solutions of s-wave scattering states for the Schrödinger equation with the Manning–Rosen potential are presented by the standard method. The normalized radial wavefunctions of scattering states on the 'k/2πscale' and the calculation formula of phase shifts are found. We also study the special case for α = 1 and find that this potential will reduce to the Hulthén potential.

In this paper, we construct an equivalent spin chain for the Gross–Pitaevskii equation with quadratic potential and exponentially varying scattering lengths using gauge equivalence. We have then generated the soliton solutions for the spin components S₃ and S⁻. We find that the spin solitons for S₃ and S⁻ can be compressed for exponentially growing eigenvalues while they broaden out for decaying eigenvalues.

This study is concerned with the chaos synchronization problem of Rössler systems subjected to multiple time delays. Based on the sliding mode control (SMC) technique, we first propose an adaptive switching surface which does not allow for a reduction of system order, as is the case in most SMC schemes. Then both a sliding mode controller and a new sufficient condition are derived to guarantee, respectively, the global hitting of the sliding mode and stability of the equivalent error dynamics in the sliding mode. Thus, the chaos synchronization for Rössler systems with multiple time delays can surely be achieved. Moreover, the proposed scheme is then applied to the secure communication system. Numerical simulations are included to demonstrate the feasibility of the proposed scheme.

It is shown that the Dirac equation for a new equal scalar and vector anharmonic oscillator potentials could be separated into a solvable angular equation and a radial equation. Corresponding exact solutions of bound states for the Dirac equation have been obtained. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is found from the boundary condition satisfied by the radial wavefunction.

In this paper, the variational iteration method (VIM) is applied to obtain the approximate analytical solution of the coupled sine-Gordon equation without any discretization. VIM is based on the incorporation of a general Lagrange multiplier in the construction of the correction functional for the equation. Comparisons with the Adomian decomposition method (ADM) reveal that VIM is very effective and convenient.

The interaction between open shells and the electron core or the core polarization of the4f⁷(⁸S)5d ⁹D_{2, 3, 4, 5}^o states in Eu⁺, has been determined by using the hyperfine anomaly. The results are compared with the experimental values and calculated hyperfine interaction integrals.

In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schrödinger from polarized optical waves in an isotropic medium. Based on the Ablowitz–Kaup–Newell–Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schrödinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented.

The nonlinear interaction of high-frequency transverse electromagnetic waves normally incident from a plasma region on to a dielectric with two surface waves (SWs) propagating in the opposite directions along the interface is studied. This interaction is found to be stable causing a slight modulation to the SWs in contrast to the decay instability for longitudinal plasma waves. The corresponding nonlinear frequency shift of the SWs is obtained and analyzed.

The distribution of molecular speeds for a hard spheres gas in the microcanonical ensemble follows the Schlüter distribution when the number of molecules is small, converging to the classical Maxwell distribution in the large number limit. We present a derivation of the Schlüter distribution, obtained from Khinchin's derivation of the factorization of the density of states, which is simpler and shorter than those currently available. We also verify its predictions for three-dimensional (3D) hard spheres using a desktop computer simulation, whereas previous studies have simulated only 2D hard discs.

We have investigated two-component spatial holographic optical solitons supported solely by cross-phase modulation of two copropagating mutually coherent optical beams in the absence of the self phase modulation effects. We have identified a wide parameter space of power and spatial widths which captures the existence of a plethora of these stationary composite solitons including a bistable variety. Additionally, we have shown that these bistable solitons can exist only if their widths are above a certain minimum value. Our analytical results have been verified by direct numerical simulation of the coupled nonlinear Schrödinger equations.

We have studied the dielectric properties of the Ba_xSr_{1- x}TiO₃ system within the framework of the transverse spin-1/2 Ising model using the effective field theory with a probability distribution technique that accounts for the self spin correlations. In particular, we have studied the critical temperature T_c(x), the polarization as function of both T and x and also the dielectric susceptibility χ(T, x) for different values of the strength of the applied electric field E.

We discuss the coupling of stationary nonlinear excitations in an electrical lattice. Due to nonlinear interaction between the modes, we show within a quasi-discrete multiple scale approach that the physics of the network is described by two coupled nonlinear Schrödinger equations. Therefore, a novel class of lattice soliton is derived in the form of a coupled kink-soliton pair. Moreover, analytical results are checked by computer experiments.

A new dynamic process, dynamic incremental scale transition (DIST), is proposed that could resolve longstanding issues in physics and cosmology. The DIST process implies that general relativity (GR) is generalized to also model discrete scale adjustments that will not alter Einstein's GR equations. A cosmos model based on the DIST process better agrees with observations than the standard cosmological model, and resolves several enigmatic cosmological puzzles including the progression of time, the connection between GR and quantum theory and the origin of inertia.

The quadrupole and monopole generalized oscillator strengths (GOS) as a function of momentum transfer are calculated for the 2p–3p and 2p–4p transitions of the neon atom using the analytical Hartree–Fock (HF) wavefunctions for the ground-state and the wavefunctions for the excited states which are obtained numerically from the modified HF Slater equation. Calculations are carried out by using the HF method and random phase approximation with exchange in the velocity formulation. The positions and the number of the extrema in the GOS have received particular attention in the evaluation. Our calculated monopole GOS of 2p–3p transition in velocity form reveals one maximum located between the experimental and theoretical results of other authors. The disagreement between our first maximum of the quadrupole GOS 2p–3p transition with the experimental and other theoretical ones is unimportant. The extrema of the monopole and quadrupole GOS of 2p–4p transition are given in this paper. The results of velocity form study also show that the electron correlation effects are important around the maxima and are found to influence the positions of the extrema insignificantly.

Transition properties of the Kα x-ray from Al through AlXII have been calculated by using relativistic configuration interaction (RCI) and the multi-configuration Dirac–Fock (MCDF) method in the active interaction approach. The contributions from Breit interaction, quantum electrodynamics (QEDs) corrections and nuclear mass corrections to the initial and final levels have been taken into account. Through the use of the active space method, the calculated values are compared with the available data on He-like and Be-like aluminium and are found to be in very good agreement with them. These data provide the reference value for level lifetime, charge state distribution and the average charge of aluminum plasma.

The electrogravitational instability of a dielectric fluid cylinder dispersed in a gravitational dielectric medium of negligible motion has been developed on using the macroscopic perturbation technique based on the normal mode analysis. The model is acting upon the pressure gradient, self-gravitating and electrodynamic (with periodic time dependent electric field) forces. For all axisymmetric and non-axisymmetric disturbances the system is governed by the Hill's second-order integro-differential equation in the disturbed surface displacement. The self-gravitating forces are destabilizing only in the axisymmetric disturbances domain 0⩽x⩽1.0668 and stabilizing in all other domains, where x is the dimensionless longitudinal wavenumber. The electric field is always stabilizing not only in the axisymmetric mode m= 0 but also in those of non-axisymmetric m≠ 0. The frequency of the time dependent periodic electric field is only destabilizing in a few axisymmetric states of perturbations while it is strongly stabilizing in the remaining axisymmetric disturbance states and also stable in all states of the non-axisymmetric perturbations. Resonance domains may arise due to the periodicity of the electric field and in some ranges of the wavenumber, the stability conditions depend solely on the frequency of the field. The self-gravitating destabilizing influence could not be suppressed whatever is the greatest value of the magnitude and frequency of the periodic electric field because the gravitational destabilizing influence will persist.

In this paper, we have studied the bounded oscillator potential for the Schrö dinger equation with the asymptotic iteration method (AIM). This work introduces a simple perturbation expansion and a new analytical expression for the energy eigenvalues. Our results have been compared with those obtained from the direct application of the AIM.

In the present paper, we propose a development to the Schwinger multichannel (SMC) method (Germano and Lima 1993 Phys. Rev.47 3976) for the elastic scattering of positrons by targets of arbitrary geometry. The essence of this work is based on the fact that the main limitation of the SMC method resides on what makes it a general method, i.e. the expansion of the scattering function is done in a L² basis (Cartesian Gaussian functions) and this is very effective only for short range potentials. Our effort now is to improve the SMC through the use of plane waves as trial functions (SMC-PW). In order to do this, we have to evaluate reliable codes involving matrix elements which are a straightforward modification of the SMC method. We also discuss a mechanism for the Buckingham potential (polarization effects) where the cutoff parameter is adjustable to the positronium formation threshold. Our results to positron-He illustrate convergence characteristics for several incident positron energies.

Periodic solutions for a parametrically excited van der Pol system with nonlinear stiffness and under state feedback control with a time delay are investigated. Two slow flow equations for the amplitude and phase of the parametric resonance response are derived. It is well known that their fixed points correspond to phase-locked periodic solutions for the starting system. In the system without control, periodic solutions exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. The stable condition for steady-state response is given by the Routh–Hurwitz criterion, but in many cases the amplitudes of periodic solutions do not correspond to the technical requirements. On the contrary, it is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude and phase can be accomplished. An effective vibration control is then possible if appropriate time delay and feedback gains are chosen.

Based on the intermediate coordinate-momentum representations, we construct the appropriate generalized Fredholm operator equation and then find its solution. The application of this equation for deriving Hermite-polynomial operator formulae is demonstrated. The connection of the generalized Wigner operator to the form of the Gaussian bivariate distribution of random variables in statistics is shown, which is useful for studying the tomogram of quantum states.

We explore stochastic resonance effects in a bistable system driven by an amplitude modulation (two-frequencies) signal and cross-correlated additive and multiplicative noises. The analytical expression of the signal-to-noise ratio (SNR) is obtained under the condition of adiabatic approximation. The results manifest: (i) the amplitude modulation deepness and the frequency of the signal affect the SNR intensely; (ii) the cross-correlation of additive and multiplicative noises leads to a novel resonance character. The multi-extrema phenomenon appears in the curve of the SNR as a function of cross-correlation coefficient λ. The SNR versus λ curve not only exhibits the multi-peaks phenomenon, but also the multi-wells phenomenon. This means that we can control the SNR by virtue of controlling λ to obtain a larger SNR under fixed noise intensities.

Observed spectral lines of neutral boron are critically compiled. From the selected best measurements, an improved and extended set of energy levels is derived for the two most abundant isotopes, ¹¹B and ¹⁰B. The ionization energy is determined to a greater precision than previously given values. The connection between the quartet and doublet term systems is revised on the basis of an isoelectronic extrapolation.

The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium.

The s-wave Schrödinger and, to clarify one interesting point encountered in the calculations, Klein–Gordon equations are solved exactly for a single neutron moving in a central Woods–Saxon plus an additional potential that provides the flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods–Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration.

Radiation of a nanosource placed in a microsphere with a quasiperiodic subwavelength spherical stack is studied. The spectral evolution of transmittance at the change of the thickness of two-layer blocks constructed following the Fibonacci sequence is investigated. When the number of layers (Fibonacci order) increases the structure of the spectrum acquires a fractal form. Our calculations show a rising strong field peak, when the ratio of width of layers in two-layer blocks of the stack is close to the golden mean value.

The spontaneous-emission branching fractions of 32 levels of Pr II were measured by the fast-ion-beam laser-induced-fluorescence technique. The levels studied had energies from ∼21 500 to ∼29 000 cm⁻¹, and the decay branches detected were in the range from 250 to 850 nm. The experimental uncertainties are within 10%. Using our previously measured radiative lifetimes, we determined the Einstein A coefficients and oscillator strengths for 260 transitions. The results are important for stellar elemental abundance determinations.

In the lattice theory of dislocation, the dislocation equation including the discreteness effect is a nonlinear integro-differential equation. It can hardly be solved. In this paper, the variational principle for the dislocation equation is presented. By using the Ritz approximation method, the variational solution is obtained, which is the same as the Peierls–Nabarro solution when the discreteness effect terms were ignored and the accurate value of the variational parameter is obtained when the discreteness effect terms were taken into account. As a natural generalization, a modified form of the sinusoidal law of force is proposed. It is found that the fine structure of the dislocation core can be predicted theoretically as long as the parameter in the modified law of force is selected properly.

Pioneer experimental indication of an extremely low alpha activity due to ¹⁵¹Eu isotope (equivalent to ∼10–70 disintegrations (h-kg of ) is discussed in the framework of a simple, one-parameter model to alpha transitions recently developed by us. The present evaluated alpha activity is found equivalent to ∼18 disintegrations(h-kg)⁻¹, in excellent agreement with the observed decay rate. Partial alpha decay half-life evaluations for ^147–153Eu isotopes are also reported.

We present formulae for the stopping power of a charged dust projectile in dusty plasmas containing the dust acoustic wave. The dependence of the test dust charge mach number (test dust charge speed/dust acoustic speed) as well as the other parameters (the plasma temperature, the dust radius) on the stopping power is discussed. It is found that highly charged dust projectiles moving with a speed much slower than the dust acoustic speed contribute mostly to the dust energy loss in dusty plasmas.