We investigate whether the recently proposed $\mathcal{PT}$-symmetric extensions of generalized Korteweg–de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can be found. The Painlevé test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable.

A freely propagating Gaussian wave packet naturally spreads with time. Exploiting the machinery of the Bohmian model of quantum mechanics, the way the wave packet spreads is re-examined.

We prove the theorem: The second-order quasilinear differential operator as a second-rank divergence-free tensor in the equation of motion for gravitation could always be derived from the trace of the Bianchi derivative of the fourth-rank tensor, which is a homogeneous polynomial in curvatures. The existence of such a tensor for each term in the polynomial Lagrangian is a new characterization of the Lovelock gravity.

A set of six invariant solutions for non-conformal perfect fluid plates in 5-flat form is obtained using one-parametric Lie group of transformations. Out of the six solutions so obtained, three are in implicit form while the remaining three could be expressed explicitly. Each solution describes an accelerating fluid distribution and is new as far as authors are aware.

It was observed that the spatiotemporal chaos in lattices of coupled chaotic maps was suppressed to a spatiotemporal fixed point when some fractions of the regular coupling connections were replaced by random links. Here we investigate the effects of different kinds of parametric fluctuations on the robustness of this spatiotemporal fixed point regime. In particular we study the spatiotemporal dynamics of the network with noisy interaction parameters, namely fluctuating fraction of random links and fluctuating coupling strengths. We consider three types of fluctuations: (i) noisy in time, but homogeneous in space; (ii) noisy in space, but fixed in time; (iii) noisy in both space and time. We find that the effect of different kinds of parametric noise on the dynamics is quite distinct: quenched spatial fluctuations are the most detrimental to spatiotemporal regularity; patiotemporal fluctuations yield phenomena similar to that observed when parameters are held constant at the mean value, and interestingly, spatiotemporal regularity is most robust under spatially uniform temporal fluctuations, which in fact yields a larger fixed point range than that obtained under constant mean-value parameters.

We numerically investigate the motion of a charged particle in a planetary magnetosphere using several kinds of equatorial plane phase portraits determined by two dynamical parameters: the charge-to-mass ratio and the 𝑧-component of the angular momentum. The dependence of chaos on any of the three factors including the two parameters and the energy is mainly discussed. It is found that increasing the energy or the absolute value of the ratio always causes the extent of chaos. However, chaos is weaker for larger

We numerically study some of the three-dimensional dynamical systems which exhibit complete synchronization as well as generalized synchronization to show that these systems can be conveniently partitioned into equivalent classes facilitating the study of bifurcation diagrams within each class. We demonstrate how bifurcation diagrams may be helpful in predicting the nature of the driven system by knowing the bifurcation diagram of driving system and vice versa. The study is extended to include the possible generalized synchronization between elements of two different equivalent classes by taking the Rössler-driven-Lorenz-system as an example.

In this study, we have investigated the asymmetry term effect for the ($p, \alpha$) and ($p, np$) reaction cross-sections and obtained new coefficients for the ($p, \alpha$) and ($p, np$) reaction cross-sections at 17.9 and 22.3 MeV energies. We have suggested semi-empirical formulas including the non-elastic effects of optical model found by fitting two parameters for proton-induced reactions. The coefficients were determined by least-square fitting method. The obtained cross-section formulas with new coefficients have been discussed and compared with the available experimental data.

The plasma generated by 1064 nm Nd:YAG laser irradiation of aluminum alloy in air at atmospheric pressure was studied spectroscopically. The electron density inferred by measuring the Stark-broadened line profile of Si(I) 288.16 nm decreases with increasing distance from the target surface. The electron temperature was determined using the Boltzmann plot method with nine strong neutral aluminum lines. Due to the thermal conduction towards the solid target and radiative cooling of the plasma as well as conversion of thermal energy into kinetic energy, the electron temperature decreases both at the plasma edge and close to the target surface. Electron density and electron temperature were also studied as functions of laser power density. At the same time, the validity of the assumption of local thermodynamic equilibrium and the effect of self-absorption were discussed in light of the results obtained.

The nonlinear response of light transmission characteristics of a liquid crystal (LC) spatial light modulator (SLM) is studied. The results show that the device exhibits a wide range of variations with different control parameters and input settings. Experiments were performed to obtain intensity modulation that is best described by either power-law or sigmoidal functions. Based on the inverse transformation, an appropriate pre-processing scheme for electrically addressed input gray-scale images, particularly important in several optical processing and imaging applications, is suggested. Further, the necessity to compensate the SLM image nonlinearities in a volume holographic data storage and retrieval system is demonstrated.

Formation of large-amplitude double layers in a dusty plasma whose constituents are electrons, ions, warm dust grains and positive ion beam are studied using Sagdeev’s pseudopotential technique. Existence of double layers is investigated. It is found that both the temperature of dust particles and ion beam temperature play significant roles in determining the region of the existence of double layers.

Plasma produced by a 355 nm pulsed Nd:YAG laser with a pulse duration of 6 ns focussed onto a copper solid sample in air at atmospheric pressure is studied spectroscopically. The temperature and electron density characterizing the plasma are measured by time-resolved spectroscopy of neutral atom and ion line emissions in the time window of 300–2000 ns. An echelle spectrograph coupled with a gated intensified charge coupled detector is used to record the plasma emissions. The temperature is obtained using the Boltzmann plot method and the electron density is determined using the Saha– Boltzmann equation method. Both parameters are studied as a function of delay time with respect to the onset of the laser pulse. The results are discussed. The time window where the plasma is optically thin and is also in local thermodynamic equilibrium (LTE), necessary for the laser-induced breakdown spectroscopy (LIBS) analysis of samples, is deduced from the temporal evolution of the intensity ratio of two Cu I lines. It is found to be 700–1000 ns.

GaAs solar cells hold the record for the highest single band-gap cell efficiency. Successful application of these cells in advanced space-borne systems demand characterization of cell properties like dark current under different ambient conditions and the stability of the cells against particle irradiation in space. In this paper, the results of the studies carried out on the effect of 8 MeV electron irradiation on the electrical properties of GaAs solar cells are presented. The $I–V$ (current–voltage) characteristics of the cells under dark and AM1.5 illumination condition are studied and 8 MeV electron irradiation was carried out on the cells where they were exposed to graded doses of electrons from 1 to 100 kGy. The devices were also characterized using capacitance measurements at various frequencies before and after irradiation. The effect of electron irradiation on the solar cell parameters was studied. It is found that only small changes were observed in the GaAs solar cell parameters up to an electron dose of 100 kGy, exhibiting good tolerance for electrons of 8 MeV energy.

An exact diagonalization calculation for a small cluster in the two-dimensional t-J model has been studied to calculate two-hole correlation. Calculations reveal dominant hole–hole correlation for holes sitting on next-nearest-neighbour (NNN) sites and critical coupling occurs at $J/t = 0.8$. With the increase in negative-type NNN hopping, correlation decreases at NNN sites whereas it increases at other sites. The thermodynamic properties such as entropy and specific heat are studied as functions of temperature with various NNN hopping strength. Results show that with the inclusion of negative NNN hopping, the system becomes more ordered. A qualitative transition temperature region has been estimated. It is shown that with the increase in NNN hopping strength, $T_{c}$ increases. Specific heat results show non-Fermi liquid-type behaviour of the system. All our calculations establish the importance of negative-type NNN hopping.

We have carried out an extensive study of electronic properties of silver iodide in 𝛽- and 𝛾-phases. The theoretical Compton profiles, energy bands, density of states and anisotropies in momentum densities are computed using density functional theories. We have also employed full-potential linearized augmented plane-wave method to derive the energy bands and the density of states. To compare our theoretical data, isotropic Compton profile measurement on 𝛾-AgI using ¹³⁷Cs Compton spectrometer at an intermediate resolution of 0.38 a.u. has been undertaken. The theoretical anisotropies are also interpreted on the basis of energy bands.