Volume 80, Issue 9

This paper intends to investigate the optical solution of the generalized nonlinear Schrodinger equation (NLSE) of higher order that includes cubic-quintic nonlinear terms and third-fourth order dispersion, focusing on the dynamics of ultra-short pulse transmission in optical fibers and quantum mechanics within the framework of nonlinear optics. The new analytical and solitary wave solutions for higher order generalized NLSE is determined with the extended G ′ G 2 $\left(\frac{{G}^{\prime }}{{G}^{2}}\right)$ -expansion method. This method is a significant mathematical instrument for identifying the exact traveling wave solution of the complex partial differential equations with greater nonlinearity and also applications in various fields of physical sciences. A variety of soliton solutions, such as periodic, plane wave and singular solutions are derived along with suitable values of the parameters. Furthermore, the examination of wave propagation through the trigonometric, hyperbolic and rational functions is represented via physical interpretation with the help of 2D and 3D surf plots. This study has a great practical significance and has the potential for broad application in several scientific domains, including nonlinear optics and quantum mechanics.

This study examines the adsorption properties of C 2 H 4 , F 2 , HCl, and H 2 S gases on 2PANI using density functional theory (B3LYP/6–311++G(d,p)). Adsorption energies follow the order: 2PANI-HCl > 2PANI-H 2 S > 2PANI-C 2 H 4  > 2PANI-F 2 including the BSSE corrections. Geometry optimizations and topological analyses (electrostatic potential, localized orbital locator and electron localization function) were performed using Multiwfn software. Mulliken charge analysis assessed the sensing potential of 2PANI for each gas. Time-dependent DFT was used to analyze molecular orbitals, reactivity indices, density of states, and UV–Vis spectra, revealing red or blue shifts depending on the gas type. The results confirm that C 2 H 4 , F 2 , HCl, and H 2 S can be physically adsorbed onto 2PANI. The recovery time and conductivity were evaluated to determine gas sensitivity performance.

This paper introduces a multistable four-scroll 3D chaotic system with amplitude control, offering a significant enhancement to the traditional four-scroll systems by allowing for dynamic adjustment of the amplitude of the chaotic oscillations. The system’s dynamics are thoroughly analyzed using equilibrium point analysis, Lyapunov exponents, bifurcation diagrams, and basins of attraction, revealing the presence of multiple stable attractors under different parameter configurations. The incorporation of amplitude control adds a new layer of flexibility, enabling the system to switch between different attractor states, including the four-scroll chaotic attractors, in a controlled manner. This multistable behavior with amplitude control is particularly valuable for applications in secure communication, chaos-based cryptography, and nonlinear signal processing. Moreover, transient chaotic behavior often emerges at certain parameter values where the system transitions between different dynamical regimes, highlighting the delicate balance between stability and chaos. An electronic circuit simulation is designed and implemented to validate the theoretical findings. The experimental results show that the circuit closely replicates the chaotic dynamics predicted by the mathematical model, including the successful realization of four-scroll chaotic attractors. The proposed system provides a promising framework for designing versatile chaotic systems with potential applications in diverse fields that require precise control over chaotic behavior.

In this paper, we combine the physics-informed derivative network (PIDN) with a progressive parameter adaptive training method (PPATM) to solve the forward problem of the Falkner–Skan equation, which originates from boundary layer fluid flow. Using the PIDN approach, we successfully obtained data-driven solutions over a broad range of parameter settings. The results of numerical simulation indicate that the error between this solution and those obtained by traditional numerical methods is relatively small, thereby verifying the effectiveness of the PIDN method in solving the Falkner–Skan equation. Moreover, by employing the PPATM training method, we extend the stable solution domain of PIDN to a very long dimensionless interval. In particular, compared with conventional physics-informed neural network (PINN) approaches, our method not only provides accurate data-driven solutions over broader parameter settings and longer intervals but also achieves stable solutions using a very small neural network, significantly reducing computational cost and complexity.

The present article is concerned with the study of cylindrical shock wave in a perfectly conducting non-ideal dusty gas influenced by magnetic field for isothermal flow in the rotating medium. The present phenomenon is governed by the hyperbolic system of non-linear partial differential equations (PDEs). To evaluate safety and predict disasters caused by explosions, it is essential to thoroughly understand the behavior of solutions to such a hyperbolic system of non-linear PDEs. To investigate all possible solutions, we have used the Lie symmetry method. Initially, we have constructed the optimal system of one-dimensional solvable Lie subalgebras. This optimal system provides vital information about group-invariant solutions, while our aim is to analyze similarity solution. The similarity solutions exist in three cases; one with exponential law shock path and two with power law shock path. Consequently, it is found that the shock wave decays with an increment in the physical parameters such as gas non-idealness, mass concentration of solid particles in the mixture, adiabatic exponent, and shock Cowling number. Also, the shock wave enhanced with an increment in the ratio of density of solid particles to initial species density of the gas. Moreover, it is found that the shock wave decays due to change in magnetic field from axial to azimuthal. The shock wave is more powerful in exponential law case in comparison to power law case.

This study investigates the parametric control of electron–positron acoustic solitons (EPAS) in a magnetized four-component quantum plasma comprising electrons, positrons, ions, and charged dust grains. Employing the reductive perturbation technique and small- k expansion method, we derive a modified Zakharov–Kuznetsov (ZK) equation to analyze the nonlinear dynamics and stability of EPAS. The phase velocity, nonlinearity, and dispersion coefficients are critically influenced by plasma parameters such as the ion-to-electron density ratio ( δ ), dust-to-electron density ratio ( μ ), positron-to-electron Fermi energy ratio ( σ ), and effective-to-ion temperature ratio ( γ ). Our results reveal that compressive and rarefactive solitons emerge depending on the interplay between restoring forces and inertia, with soliton amplitude and width exhibiting distinct trends under varying parametric conditions. The instability growth rate of EPAS is also examined, demonstrating sensitivity to magnetic field strength and propagation angle. These findings bridge theoretical plasma physics with astrophysical observations, offering insights into wave behavior in environments like neutron star magnetospheres and white dwarf atmospheres. The study underscores the role of quantum degeneracy, relativistic effects, and dust-induced charge depletion in shaping nonlinear wave phenomena.

An important aspect of the study of nonlinear processes is the examination of integrable nonlinear evolution equations. This paper concerns propagation phenomena for the integrable (2 + 1)-dimensional Bogoyavlenskii’s breaking soliton equation. We employ the Bernoulli sub-ODE approach to find travelling wave solutions for these integrable nonlinear systems. The findings demonstrate that the model used in this study provides various explicit travelling wave solutions. We also examine how the parameters of the solutions affect the wave propagation speed. Suitable parameter values are selected to depict the obtained explicit soliton solutions graphically. In 2D and 3D graphs, the behaviour of the solitary wave patterns is shown. Additionally, an in-depth examination of the stability properties of the system is undertaken, employing bifurcation analysis techniques to elucidate the behaviour of the system under varying parameter values. Moreover, the research delves into the construction of phase portraits, allowing for a comprehensive visualization of the dynamics, while concurrently presenting analytical solutions for the planar system being investigated. Furthermore, the study employs rigorous mathematical methods to explore the bifurcation behaviour of the breaking soliton equation, enabling a thorough understanding of complex dynamical characteristics, with a focus on their phase portraits and associated solutions. To ensure the accuracy of the obtained solutions, we performed a validation process using Maple software, where we reintroduced the solutions back into their respective original equations.

The nuclear structure properties of even–even nuclei is analyzed using the relativistic mean field (RMF) model with DDME2 interactions. Key nuclear characteristics, including binding energy ( E b ), neutron separation energies ( S n , S 2 n ), the root mean square (rms) radii of protons ( R p ), neutrons ( R n ), charge distributions ( R c ), quadrupole deformation parameter ( β 2 ), and potential energy curves, are thoroughly examined. The β 2 values, one taken from the finite range droplet model (FRDM) and other computed using the RMF model with DDME2 interactions, are incorporated as input parameters in the proton–neutron quasiparticle random phase approximation (pn-QRPA) model to assess the β -decay characteristics of isotopes such as 92 Pd, 94 Pd, 96 Cd, 98 Cd, 100 Sn, and 102 Sn. This study explores β -decay properties such as half-lives, Gamow–Teller strength distributions, and stellar decay rates. Comparisons with experimental data reveal a strong correlation. The combined effects of β + decay and electron capture (EC) play a crucial role in high-temperature and high-density environments, with reaction rates increasing by up to five orders of magnitude as stellar density rises from (10 7 to 10 11 ) g/cm 3 . These findings offer significant contributions to the understanding of massive star evolution during its final stages.

A spin and angular momentum dependent version of a mass formula for mesons and baryons is derived by relating the eigenvalue solutions of Heim’s quantum field theory, which reproduce the results of Mac Gregor’s phenomenological model of particle masses, and which are compatible with the existence of magnetic charge, to the interaction energy of a quark/dyon model with magnetic charge. To do this, Schwinger’s ’magnetic model of matter’ is expanded by assuming that its dyons are constituent quarks with a magnetic charge distribution, and thus with magnetic dipole moments and currents. The derived strong interaction energy reproduces the known Breit–Fermi potential, but also provides a Zeeman–/Paschen–Back-like term which can describe respective patterns especially in the mass spectrum of the isoscalar mesons. Based on the non-linear quantum field theory, whose poly-metric approach merges with General Relativity in the macroscopic limit, the model “explains” the masses of the charged leptons, heavy bosons and hadrons – and for the latter, composed in the dyon model, now in an angular momentum dependent form.

The temperature-dependent elastic, mechanical, and thermoacoustic properties of transition metal carbide TMCs (TM = Ti, Zr, Hf) have been widely analyzed. The second-, third-, and fourth-order elastic constants are calculated via Coulomb and Born–Mayer potential model in the temperature range of 0–500 K, which confirm the elastic stability of the selected materials. The mechanical constants and ultrasonic velocities are obtained from the second-order elastic constants. Pugh’s ratio and Poisson’s ratio have confirmed that TiC, ZrC, and HfC exhibit brittle nature at room temperature. Additionally, the thermoacoustic properties including Debye temperature, thermal conductivity, thermal relaxation time, acoustic coupling constant, and ultrasonic attenuation are investigated for selected TMCs along ⟨100⟩, ⟨110⟩, and ⟨111⟩ directions. The Debye velocity and Debye temperature attained their highest values along the ⟨100⟩ orientation. The ultrasonic attenuation is mainly governed by the Akhiezer mechanism rather than the thermal relaxation mechanism in present study. The calculated parameters are compared with other B1 structured materials, presenting a comprehensive evaluation of the performance of TiC, ZrC, and HfC.