In this paper, we study Klein–Gordon–Zakharov equations which describe the propagation of strong turbulence of the Langmuir wave in a high-frequency plasma. Using the symbolic manipulation tool Maple, the classifications of symmetry algebra are carried out, and the construction of several local non-trivial conservation laws based on a direct method of Anco and Bluman is illustrated. Starting with determination of symmetry algebra, the one- and two-dimensional optimal systems are constructed, and optimality is also established using various invariant functions of full adjoint action. Apart from classification and construction of several conservation laws, the Painlevé analysis is also performed in a symbolic manner which describes the non-integrability of equations.

This paper presents the cylindrical gate-all-around (GAA) silicon on insulator (SOI) FinFET, which not only eliminates the corner effect but also shows high on-drain current $(I_{\rm{ON}}) (\sim 10^{−2} \rm{A})$, low leakage current $(I_{\rm{OFF}}) (\sim 10^{−10} \rm{A})$, high $I_{\rm{ON}}/I_{\rm{OFF}} (10^{8}$ > $10^{6})$ and reduced subthreshold swing (SS) (64.55 mV/dec, which is nearest to the Boltzmann limit of 60 mV/dec). To have a better understanding of the working principles, analytical modelling of electrical parameters such as surface potential, threshold voltage, drain current and SS hasbeen carried out by solving two-dimensional Poisson’s equation using superposition principle. The behaviour of threshold voltage, drain current and SS has been investigated for different dimensional and electrical parameters such as channel lengths, channel radius, gate work functions, dielectric constants, drain-to-source voltages andchannel concentrations. The physics-based models have been cross-examined with extracted three-dimensional TCAD simulation results. The modelled values show good agreement with the simulated data. Moreover, analogue performances such as transconductance, output conductance, intrinsic gain and gate capacitance for differentchannel lengths and radii of the presented device are also studied.

We investigate numerically the responses of the single pendulum and double pendulum arms coupled to a nonlinear RLC-circuit shaker through a magnetic field. These systems can be used to build a robotic device or an automat. The nonlinear RLC circuit is a Duffing oscillator that generates electric bursting oscillations. We first examine the dynamical behaviour of the single pendulum arm. Time series shows that the pendulum arm exhibits bursting oscillation. When the natural frequency $w_{2}$ < 1, the shape of the bursting in the electrical part is different from that observed in the pendulum arm and if $w_{2}$ > 1, the shape is the same. We then explore the behaviour of a double pendulum arm powered by electric bursting oscillations. Time series are also used to explore the behaviour of each pendulum arm. The results show that the displacement of each pendulum arm undergoes bursting oscillations resulting from the transfer of the electronic signal. The shape of bursting of the first pendulum is different from that of the second pendulum for some values of $w_{1}$. The shape, period and amplitude of the bursting oscillations depend on various control parameters.

A complex network and chaos-based method, based on the visibility graph algorithm, is applied to study particle fluctuations in $\pi^{−}$–AgBr interactions at 350 GeV with respect to the shower multiplicity dependence. The fractal structure of the fluctuations is studied by using the power of scale freeness of visibility graph (PSVG). The selection of visibility graph as the type of complex network for our analysis is justified as this algorithm gives the most precise result with finite number of data points and this experiment has finite number of events. The topological parameters along with PSVG values are extracted and analysed. The analysis shows that the fractality character is weaker for the lowest multiplicity bin and is stronger for the highest multiplicity bin.

The present study discloses the evaluation of second-order elastic constants of wurtzite boron nitride(w-BN) at room temperature and at different pressures using the many-body interaction potential model approach. Orientation- and pressure-dependent ultrasonic velocity, thermal relaxation time and other related thermophysical parameters (Debye temperature, Debye average velocity, specific heat and thermal energy density) are also calculated using the evaluated second-order elastic constants. The orientation-dependent thermal relaxation time of w-BN is predominantly affected by the Debye average velocity and is indirectly governed by second-order elastic constants. Thermal relaxation time of w-BN is found to decrease with pressure. Calculated elastic and ultrasonic properties of w-BN are compared with the properties of other wurtzite structured materials for a complete analysis and characterisation of the material.

The halo structure of a nucleus is investigated on the basis of separation energy consideration and potential energy calculations. Most of the predictions on the existence of halo nuclei are found to agree with the available experimental studies. For the first time, the possibility of emitting proton halo (p-halo) nuclei from heavy nuclei within the range $82 \leq Z \leq 102$ has been studied by evaluating decay half-lives for the emission of 1p-halo nuclei $^{8}\rm{B}, ^{12}\rm{N}, ^{13}\rm{N}, ^{17}\rm{F}$ and 2p-halo nuclei $^{9}\rm{C}, ^{17}\rm{Ne}, ^{18}\rm{Ne}, ^{20}\rm{Mg}$ using Coulomb and proximity potential model (CPPM). Of these, the emissions of 1p-halo nuclei $^{8}\rm{B}, ^{12}\rm{N}, ^{13}\rm{N}$ and $^{17}\rm{F}$ are found to be probable from various heavy nuclei as the half-lives of the corresponding emissions are within the experimental upper limit $(T_{1/2} \leq 10^{30} s)$. When dealing with 2p-halo nuclei, its emission is observed to be less probable compared to 1p-halo nuclei, except $^{18}\rm{Ne}$. Compared to the probability of emission of a normal cluster, the probability of emission of a p-halo nucleus from a radioactive nuclide is found to be less but still, there is a finite probability of p-halo emissions from heavy nuclei.

The current work demonstrated a new technique to improve the accuracy and computational efficiency of the nonlinear partial differential equation based on the homotopy perturbation method (HPM). In this proposal, two different homotopy perturbation expansions, the outer expansion and the inner one, are introduced based on two different homotopy parameters. The multiple-scale homotopy technique (He-multiple-scalas method) is applied as an outer perturbation for the nonlinear Klein–Gordon equation.A highly accurate periodic temporal solution has been derived from three orders of perturbation. The amplitude equation, which is imposed as a uniform condition, is of the fourth-order cubic–quintic nonlinear Schrödinger equation. The standard HPM with another homotopy parameter has been used as an inner perturbation to obtain a spatial solution of the nonlinear Schrödinger equation. The cubic– quintic Landau equation is obtained in the inner perturbation technique. Finally, the approximate solution is derived from the temporal and spatial solutions. Further, two different tools are used to obtain the same stability conditions. One of them is a new tool based on the HPM, by constructing the nonlinear frequency. The method adopted here is important and powerful for solving partial differential nonlinear oscillator systems arising in nonlinear science and engineering.

We explore the dynamics of quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux term, which arise in well-known physical and biological problems such as population dynamicsof the species. Three integration techniques, namely the $(G'/G)$-expansion method, its generalised version and Kudryashov method, are adopted to solve these equations. We attain new travelling and solitary wave solutions inthe form of Jacobi elliptic functions, hyperbolic functions, trigonometric functions and rational solutions with some constraint relations that naturally appear from the structure of these solutions. The travelling population fronts,which are the general solutions of nonlinear diffusion–reaction equations, describe the species invasion if higher population density corresponds to the species invasion. This effort highlights the significant features of the employed algebraic approaches and shows the diversity in the constructed solutions.

In this paper, we investigate the three coupled variable-coefficient nonlinear Schrödinger equations, which describe the amplification or attenuation of the picosecond pulse propagation in the inhomogeneous multicomponent optical fibre with different frequencies or polarisations. Based on the Darboux dressing transformation, semirational rogue wave solutions are derived. Semirational rogue waves, Peregrine combs and Peregrine walls are obtained and demonstrated. Splitting behaviour of the semirational Peregrine combs and attenuating phenomenon of the semirational Peregrine wall are exhibited. Effects of the group velocity dispersion, nonlinearity and fibre gain/loss are discussed according to the different fibres.We find that the maximum amplitude of the hump of the semirational rogue wave is less than nine times the background height due to the interaction between the soliton part and rogue wave part. Further, there is a bent in the soliton part of the semirational rogue.

In this paper, three nonlinear differential-difference equations (NDDEs) from the same hierarchy are investigated using the generalised perturbation $(n, N − n)$-fold Darboux transformation (DT) technique. The dark multisoliton solutions in terms of determinants for three equations are obtained by means of the discrete $N$-fold DT. Propagation and elastic interaction structures of such soliton solutions are shown graphically. The details of their evolutions are studied through numerical simulations. Numerical results show the accuracy of our numerical scheme and the stable evolutions of such dark multisolitons without a noise.We find that the solutions of lower-order NDDEs in the same hierarchy are more robust against a small noise than their corresponding higher-order NDDEs. The discrete generalised perturbation $(1, N − 1)$-fold DT is used to derive some discrete rational and semirational solutions of the first equation, and a few mathematical features are also discussed. Results in this paper might be helpful for understanding some physical phenomena.

In this paper, the spectral properties of temporal double pulses centred at the same central wavelength and two different central wavelengths are numerically presented based on hydrogenated amorphous silicon core optical fibre. In order to characterise the output spectra of double pulses, the group velocity dispersion and various nonlinear processes including self-phase modulation, cross-phase modulation, two-photon absorption, free carrier absorption and free carrier dispersion are considered in the theoretical model. Numerical results show that, under fixed fibre length condition, the widths of the outcome spectra are strongly dependent on the delay times, peak powers and initial chirps of input double pulses, i.e. widths of the output spectra are proportional to the launched peak powers, and the delay times control the separation between two pulses, resulting in the spectral change within a proper delay time, and the spectral widths are compressed or extended by judiciously adjusting the initial chirps imposed on the input pulses.

This paper aims to provide stability and thermomechanical analysis of hydromagnetic Falkner–Skan Casson conjugate fluid flow over an angular–geometric wedge-shaped surface. Based on the Buongiorno’s model,the governing boundary-layer equations are derived and solved iteratively using the homotopy analysis method (HAM). Furthermore, the HAM-series solution is optimised by minimising its squared residual errors. It is shown that the proposed approach can serve as an efficient criterion for accurately solving nonlinear problems.

The limitation of traditional microring mode resonance, the microsphere confocal cavity is the best candidate for a low loss and controllable linewidth. Based on the transform matrix method, we investigate the waveguide coupled to a microsphere whispering-gallery mode (WGM) system. We find that the confocal cavity mode iscompletely different from the traditional ring cavity mode. The confocal cavity mode is excited in asymmetrical dual microsphere systems, and the spectrum of asymmetrical dual microsphere systems appear as an electromagnetically induced transparency (EIT)-like profile, whereas the spectrum of symmetrical dual microsphere systems appears as Lorentz profile. The traditional ring cavity mode is excited in the symmetrical single microsphere system.