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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,...
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...
A complex network and chaos-based method, based on the visibility graph algorithm, is applied to study particle fluctuations in $$\pi ^{-}$$ π- –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...
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...
In this paper, three nonlinear differential-difference equations (NDDEs) from the same hierarchy are investigated using the generalised perturbation $$(n,N-n)$$ (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...
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,...
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 is completely different from the traditional ring cavity mode. The confocal cavity...
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 $$82 \le Z \le 102$$ 82≤Z≤102 has been studied...
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 dynamics of the species. Three integration techniques, namely the $$({G^\prime }/{G})$$ (G′/G) -expansion method, its generalised version and Kudryashov method, are adopted to solve these equations...
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...
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 ($$I_{\mathrm{ON}}$$ ION ) ($$\sim \!\!10^{-2}~\mathrm{A}$$ ∼10-2A ), low leakage current ($$I_{\mathrm{OFF}}$$ IOFF ) ($$ \sim \!\!10^{-10}~\mathrm{A}$$ ∼10-10A ), high $$I_{\mathrm{ON}}$$ ION $$/$$ / $$I_{\mathrm{OFF}}$$ IOFF...
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...
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...
Magnetic resonance imaging (MRI) is used in physics, chemistry, engineering and medicine to study complex materials. In this paper, numerical solution of fractional Bloch equations in MRI is obtained using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). Sufficient conditions for the convergence of FVIM and its error estimate are established...
Steady State Tokamak-2 (SST-2) will be an intermediate fusion machine before Indian DEMOnstration power reactor (DEMO) development to realise the reactor technologies. It is designed for fusion gain $$Q=5$$ Q=5 and fusion power in the range of 100–300 MW. Nuclear design analyses of SST-2 machine have been carried out to support the conceptual design work. Analyses have been carried out for two breeding...
In this paper, we discuss a new fractional-order memristor-based three-dimensional chaotic system with a stable equilibrium point. The proposed system belongs to the category of hidden attractors dynamical system. The system is new in the sense that it is a fractional-order memristor-based chaotic system and exhibits hidden attractors. The chaotic behaviour of the system is accessed by various numerical...
In this paper, a passive control scheme based on the fractional-order calculus is proposed. We study the modified complex projective synchronisation between two identical fractional-order complex chaotic systems, and its application in the secure communication. The fractional-order complex chaotic Lorenz system is employed to encrypt the emitted signal. In the transmitter module, the information signal...
In this paper, we employ the improved homoclinic test technique and the extended homoclinic test technique. With the help of the symbolic calculation and applying the improved methods, we solve the $$(3+1)$$ (3+1) -dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation to obtain some new periodic kink-wave, periodic soliton and periodic wave solutions.
We propose a pseudopotential of Kumar form with two parameters, the core radius ($$r_{\mathrm{c}}$$ rc ) and the model radius ($$r_{\mathrm{m}}$$ rm ), which in practice is reduced to a single-parameter potential taking $$r_{\mathrm{m}}$$ rm as the experimental atomic radius. The validity of the presently used pseudopotential is verified by carrying out a detailed study of transport properties of...
The current study deals with the influence of a uniform electric field on a cylindrical streaming sheet. This paper investigates a few representatives of porous media. These media are considered to be uniform, homogeneous and isotropic. The analysis is based on viscous potential theory, which assumes that the viscous forces affect only the interface between the fluids. The mathematical treatment is...
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