In this paper, the classical Lie group method is employed to obtain exact travelling wave solutions of the generalized Camassa–Holm Kadomtsev–Petviashvili (g-CH–KP) equation. We give the conservation laws of the g-CH–KP equation. Using the symmetries, we find six classical similarity reductions of g-CH–KP equation. Many types of exact solutions of the g-CH–KP equation are derived by solving the reduced equations.

This paper investigates, for the first time, the applicability and effectiveness of He’s semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He’s semi-inverse variational principle method and the ansatz method are used to construct exact solutions of nonlinear fractional Klein–Gordon equation and generalized Hirota–Satsuma coupled KdV system. These equations have been widely applied in many branches of nonlinear sciences such as nonlinear optics, plasma physics, superconductivity and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theoretical and numerical studies.

An application of the $(G'/G)$-expansion method to search for exact solutions of nonlinear partial differential equations is analysed. This method is used for Burgers, Fisher, Huxley equations and combined forms of these equations. The $(G'/G)$-expansion method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the $(G'/G)$-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

We show that for the quantum mechanical problem which admit classical Laguerre/Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the potential. Then, we claim that the existence of these exceptional polynomials leads to the presence of non-trivial supersymmetry.

We consider a model for insect–pathogen interaction where the insect population is divided into two groups, one group susceptible to disease and other resistant to disease. An individual born susceptible to or resistant to disease depends on the local population levels at the start of each generation. Here we consider density-dependent models of transmission because we characterize diseases that spread through environmental propagules or through random contact among individuals. We consider the case where the fraction of resistant individuals increases as the total population increases. White and Wilson (Theor. Popul. Biol. 56, 163 (1999)) have reported the results of density-dependent monotonic increase of resistance class by choosing a particular type of function. In this paper, we have chosen a class of monotonic density-dependent resistance functions and studied their effects on insect–pathogen dynamics. In particular, we have investigated the effects of different types of monotonic density-dependent resistance on the bistable nature of the model. Numerical simulation results are presented and interpreted.

We analyse and explore some peculiar features of the generalized Pöschl–Teller potential. This particular potential can be tuned in terms of the allowed number of excited states, the shape of the potential, and the strength of the confinement. As an application we investigate the Bose–Einstein condensation of noninteracting ³⁹K atoms in this trapping potential. We numerically study the effect of different tuning schemes of this particular potential on the dynamics of noninteracting BEC.

Dynamics of fractional-order memristor circuit system and its control are investigated in this paper. With the help of stability theory of fractional-order systems, stability of its equilibrium points is analysed. Then, the chaotic behaviours are validated using phase portraits, the Lyapunov exponents and bifurcation diagrams with varying parameters. Furthermore, some conditions ensuring Hopf bifurcation with varying fractional orders and parameters are determined, respectively. By using a stabilization theorem proposed newly for a class of nonlinear systems, linear feedback controller is designed to stabilize the fractional-order system and the corresponding stabilization criterion is presented. Numerical simulations are given to illustrate and verify the effectiveness of our analysis results.

Measurements of 1064 nm laser-induced egg shell plasma parameters are presented in this paper. Of special interests were its elemental identification and the determination of spectroscopic temperature and electron density. The electron temperature of 5956 K was inferred using an improved iterative Boltzmann plot method with six calcium atomic emission lines, and the electron number density of 6.1 × 10¹⁶ cm⁻³ was determined by measuring the width of Stark-broadened once-ionized calcium line at 393.37 nm. Based on the experimental results, the laser-induced egg shell plasma was verified to be optically thin and satisfy local thermodynamic equilibrium (LTE). Furthermore, experiments also demonstrated that the loss of energy due to the reflection of the laser beam from the plasma can be neglected and the inverse bremsstrahlung (IB) absorption was the dominant mechanism of plasma heating at the IR wavelength.

Using the ABCD matrix method, the common stability region between the sagittal and tangential planes of a four-mirror Kerr lens mode-locked (KLM) laser cavity is obtained for different ranges of input power. In addition, the effect of the input power on the Kerr lens sensitivity is investigated. Optimal input power and position for highest Kerr lens sensitivity in the stability region are presented and self-starting regime has been achieved. Results show that the resonator input power has a great influence on designing the KLM lasers which can be used in fabricating an optimal femtosecond laser.

A mathematical model is developed to analyse the peristaltic flow of couple-stress fluid in an inclined asymmetric channel with convective conditions. Soret and Dufour and Hall effects are taken into account. Analysis has been carried out in a wave frame of reference. Expressions for velocity, pressure gradient, temperature and concentration are constructed. Pumping and trapping phenomena are examined. Impact of sundry parameters on the velocity, temperature and concentration is discussed.

In the present study, X-ray emission dose characteristics from a small Mather-type PF device in various pressures of argon as the operating gas were studied. The PF device was powered by a 12 𝜇F capacitor at 25 kV charging voltage. Time-integrated hard X-ray (HXR) emission was investigated using thermoluminescence dosimeters (TLDs). These detectors were calibrated with ⁶⁰Co and ¹³¹Cs sources. Twenty-four dosimeters were placed at four different radial distances from the axis of the electrodes at the top of the anode to measure the dose spatial distribution at the top of the anode for different pressures (0.5–1.3 mbar). At each radius, six dosimeters were placed circularly with equal angular intervals on the inner surface of the device chamber. It was found that the optimum pressure for the highest yield of X-ray is 0.9 mbar. The maximum measured dose was 17 mGy per shot at the top of the anode and about 0.5 mGy per shot at 90° with respect to the anode axis. Furthermore, these results showed that the dose at each radius is symmetrical at 360° around the top of the anode, but X-ray distribution follows an anisotropical behaviour. A fast plastic scintillator was also used for time-resolved HXR detection, and a linear relation was observed between the amplitude of the scintillator-PMT signals and TLD responses.

We derive the trial Hall resistance formula for the quantum Hall metals to address both the integer and fractional quantum Hall effects. Within the degenerate (and crossed) Landau levels, and in the presence of changing magnetic field strength, one can invoke two physical processes responsible for the electron conduction and quantum Hall effects in Fermi metals. One of the process requires the Pancharatnam wavefunction transformation, while the second involves electron transfer between two orthogonalized wavefunctions (within the degenerate and crossed Landau levels). We discuss the relevant physical postulates with respect to these physical processes to qualitatively reproduce the measured Hall resistance’s zigzag curve for both the integer and the fractional filling factors. Along the way, we give out some evidence to contradict the postulates with experiments.

Transportation infrastructure plays a vital role in the development of a country’s economy and is regarded as one of the most important indicators of its economic growth. In this study, we analyse the Airport Network of Pakistan (ANP), which represents Pakistan’s domestic civil aviation infrastructure, as a weighted complex network. We find that ANP is a small-world network and is disassortative in nature. We further analyse the dynamic properties of the network and compare them to their topological counterparts. Although small in size, the ANP does show similar properties as compared to the US, China and especially the Indian airport network.