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We investigate the dynamics of ultrashort pulses in a real-world system featuring periodically distributed dispersion and nonlinearity. We present a precise solution resembling a chirped soliton for the higher-order nonlinear Schrödinger equation (HNLS). This solution incorporates group velocity dispersion (GVD), stimulated Raman scattering (SRS), a third-order dispersion (TOD) term, cubic nonlinear effects and self-steepening (SS) effects with spatially varying coefficients. The derivation is based on specific parametric conditions, accounting for both linear and nonlinear absorption and amplification. The investigation reveals the stability of solitary-like solutions as they propagate over long distances in the medium. Additionally, we furnish parametric conditions that dictate the existence of chirped solitons. The numerical results closely corroborate the outcomes obtained through analytical approaches.

In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., (H = H_1 + H_2), where (H_1) and (H_2) are the Hamiltonians of two one-dimensional unit-mass oscillators. It is shown that there exists a third functionally-independent first integral (Theta ), ensuring superintegrability. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into two isolated (non-interacting) one-dimensional oscillators.

Heat absorption and thermal radiation have significant roles in engineering and research. These two principles have applications in thermal transportation, gas turbines, nuclear power plants, electrical fuel, aerospace engineering, projectiles and renewable energy. The present work analyses the stagnation point ternary nanofluid motion over a circulating sphere in the presence of a magnetic field and radiation absorption. The nonlinear controlling equations are replaced by ordinary differential equations by applying a suitable comparison factor. The bvp4c process was used to establish numerical outcomes of the partial differential equations. This mathematical numerical findings are presented graphically. The results of ternary nanoparticles (Cu–Ag–CuO/water), hybrid nanoparticles (Cu–Ag/water) and copper (Cu) nanoparticles have also been compared, and this comparison suggests that ternary nanoparticles (Cu–Ag–CuO/water) are more effective at attenuating hemodynamic factors (such as wall shear stress and heat transfer) than hybrid and copper (Cu) nanoparticles. Comparison with previous literature results is also done and the results are found to be in very good agreement with those published earlier.

The stochastic resonance (SR) phenomenon for a bistable system subject to signal-modulated noise and to multiplicative and additive noise is investigated. The signal is modelled as a random-phase asymmetric square-wave one. Based on adiabatic approximation condition and two-state theory, the system output signal-to-noise ratio (SNR) is deduced. It is found that double SR phenomenon occurs when the SNR varies with the asymmetry of the square-wave signal. One resonance peak appears when the SNR changes with the amplitude of the square-wave signal. Traditional SR can be observed on the curves of the SNRs vs. the strength of the signal-modulated noise and vs. the intensities of the multiplicative and additive noise. The non-monotonous dependence of the SNR on the system parameter is discussed.

A study is carried out for the flow of a steady two-dimensional hybrid nanofluid through an exponentially expanding/shrinking surface under the influence of a magnetic field. Further, the impact of thermal buoyancy is also incorporated into the momentum equation. The model is developed using the rheological properties of hybrid nanofluid, such as viscosity, conductivity, specific heat, etc. that develop the physical significance of nanofluid. The principal equations for the motion are re-constructed to their dimensionless form by implementing similarity transformation and these are handled numerically using Runge–Kutta fourth-order. The crux of the problem is that the dual solution is obtained for the particular flow parameters. Further, the simulation is carried out by setting the characterising parameters, and their characteristics are explained briefly. The important outcomes of the study are: for the enhanced volume concentration the velocity profile enhances significantly in the case of the first solution and the impact is opposite in the case of the second solution.

In this paper, we numerically investigate a tunable and switchable metamaterial absorber operating in the mid-infrared region. The metamaterial structure comprises an array of metal–dielectric concentric nanodisks and a metal square patch on a substrate coated with thin dielectric and metal layers. The two dielectric regions induce two absorption bands, which can be independently tuned by changing the refractive index and geometrical parameters of the dielectric layers. In an optimised geometry, a dual-band to a single-band switchable frequency response is achieved by interchanging the refractive index of the dielectric layers. The origin of the resonant absorptions is traced to the simultaneous excitation of electric and magnetic fields in the dielectric regions. Due to architectural symmetry, the investigated structure is polarisation-insensitive and exhibits high absorption over a wide range of angles.

In this paper, we studied the thermodynamic quantities of dyonic ModMax and Taub-NUT black holes (BHs) to investigate their universal relations, viz. that product formulas are mass-independent. So, we calculated the thermodynamic parameters of these BHs in the inner and outer event horizons. We also obtained information about the left and right central charges. We showed that the central charges are not independent of the mass, i.e., they do not correspond to the conformal field theory (CFT). Also, we showed that the two sides of the central charge for the Taub-NUT BH are the same. These results play an important role in improving AdS/CFT and holography and thermodynamic studies. Finally, we compared our results with the other works in the literature.

The parametrization of the oblique corrections through S, T, and U – later extended by V, W and X – is a convenient way of comparing the predictions for various electroweak observables at the one-loop level between the Standard Model and its extensions. That parametrization assumes that the extensions under consideration have ({SU(2)times U(1)}) gauge symmetry and the tree-level relation (m_W = m_Z cos {theta _W}) between the Weinberg angle and the gauge-boson masses. In models where that relation does not hold at the Lagrangian level, the parameter T is not ultraviolet-finite, making the parametrization inadequate. We present expressions that parametrize the difference of the various predictions of two models with (m_W ne m_Z cos {theta _W}) in terms of oblique parameters. The parameter T does not play a role in those expressions. Conveniently, they may be reached from the ones that were derived for models with tree-level (m_W = m_Z cos {theta _W}), by performing a simple substitution for T. We also discuss the difficulties in using oblique parameters when comparing a model with (m_W ne m_Z cos {theta _W}) to the Standard Model. Finally, we compute the relevant five oblique parameters S, U, V, W and X in the SM extended by both, hypercharge (Y=0) and (Y=1), triplet scalars.

The study of the static properties of isotopes, such as ground-state energy of the system and the energy spectra, electric quadrupole, as well as charge radii and so many others, is one of the significant areas of interest in nuclear physics. Therefore, in this field, the ground-state energy of a nucleus is an essential part of the study. In addition, understanding the nuclear force depends critically on understanding the nuclear charge radii. In this work, we considered Li isotopes in the study of two-body system configuration, and then we calculated the ground-state energy and charge radii for some of them.