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The scattering phenomena can be realized in a variety of everyday situations, including the rainbow pattern after a rainstorm, the dispersion of raindrops, information and communication (ICT) systems, radar cross section (RCS) measurement, and remote sensing. Inspired by the electromagnetic scattering features, this study explores the scattering characteristics of orbital angular momentum (OAM) carried by Gaussian vortex beam (GVB) for perfect electromagnetic conductor (PEMC) sphere by utilizing the generalized Lorenz–Mie theory (GLMT). Stemming from the integral localized approximation (ILA) method, the beam‐shape coefficients (BSCs) representing the incident GVB are obtained. Vortex beams carry distinct unique optical characteristics as compared to the other beam types as these possess OAM. Computations for the efficiencies (scattering and extinction) for a focused GVB are conducted and discussed to analyze the scattering phenomena of the electromagnetic fields outside the PEMC sphere. To ensure the accuracy of the results, scattering efficiency for Gaussian beam and plane wave is computed and compared using the GLMT for PEMC sphere. The OAM mode index, beam waist radius, and the scalar admittance of GVB are chosen as parameters to investigate their impact on the scattering dynamics (i.e., scattering and extinction efficiency). The numerical results show that OAM mode index, beam waist radius, and PEMC admittance have greater impact on optical efficiencies. Nonetheless, the trend of the scattering efficiency decreases irrespective of the extinction efficiency i.e., increases for OAM mode index. [ABSTRACT FROM AUTHOR]

This study examines the (3 + 1) dimensional extended quantum Zakharov–Kuznetsov equation in weakly nonlinear ion-acoustic phenomena and quantum electron-positron-ion magneto plasma. For accomplishing this goal, two distinct mathematical approaches namely new mapping method and new Kudryashov's method are fashioned. These solutions encompass dark, bright, singular, periodic singular, and some other rational solutions. Graphical depictions of some obtained solutions by 2D, 3D and contour plots meticulously crafted within figures offered profound insights into the deep physical appearances of the structures under examination. Our outcomes highlight that the proposed methods assist as an efficient and inclusive approaches to discover the solitons for the present model. The comparison with previous papers highlights that the methods employed in our study are being utilized for the first time within the context of the extended quantum Zakharov–Kuznetsov equation which underscores the novelty of our paper. By retaining these two methods, we not only boost our consideration of the dynamical behavior of these kind of models but also provide a useful tool for finding specific soliton solutions of nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The scattering of x linearly polarized non-diffracting Lommel beam by a perfect electromagnetic conductor (PEMC) sphere is analyzed within the generalized Lorenz–Mie theory (GLMT) framework. The electromagnetic fields of the incident Lommel beams are expressed by employing spherical vector wave functions (SVWFs) and beam shape coefficients (BSCs). These BSCs are mainly considered in the expression of shaped beams in the GLMT with slight beam axicon angle. The scattered electromagnetic fields are constructed using unknown scattering field coefficients (SFCs) and SVWFs. These undetermined SFCs are calculated employing boundary conditions (BCs) at the PEMC surface. The expressions of the far-region/far-zone scattering intensity (FSI) are given and computed. The influences of Lommel beam configuration parameters like as beam order, beam half cone angle, beam asymmetry parameter, beam center coordinates positions, and PEMC sphere size parameter in addition to PEMC scalar admittance on the FSI are analyzed and discussed. The experience of this research work will be quite helpful in analyzing optical radiation force and torque, electromagnetic scattering, light manipulation, antenna engineering domain, optical tweezers, particle interaction, and trapping. Moreover, findings of the study can also be extended to study the interaction between the non-diffracting Lommel beam and the metamaterial structures. [ABSTRACT FROM AUTHOR]

In this work, we use symbolic computation and ansatz function schemes, to investigate the soliton solutions for the nonlinear Schrödinger equation (NLSE) along with Kudryashov's quintuple self-phase modulation system (KQSPMS) including dual-form of nonlocal nonlinearity (DFNLN). We initially determine the ordinary differential (OD) form for this model through a variable transformation. Then we introduce numerous new dynamical soliton types: the M-shaped rational soliton, the M-shaped interaction between one and two stripe solitons, the periodic cross-M-shaped rational (PCMR) soliton, the periodic cross-kink (PCK) soliton, multi-waves, and the homoclinic breather soliton. Secondly, we determine the partial differential (PD) form for this model through a variable transformation. Moreover, a lump soliton, a periodic wave, a rogue wave, a lump interaction with a periodic and kink wave, and three different types of breather soliton will obtain. We'll demonstrate these solutions' unique structure and extremely interesting interaction behavior. We'll also use graphs (3-D and contour plots) to discuss the dynamics of the results after setting the parameters to the proper values. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger–Poisson equation with gravitational potential field is examined, along with its many soliton interactions and travelling wave solutions. By applying Hirota Bilinear scheme, we will give a brief study on transformation of solitons, also by Sine–Gordon expansion scheme solitary travelling wave solutions will be obtained in terms of trigonometric and hyperbolic functions. The innovative Hirota bilinear method is a powerful and standard technique, play a crucial role in producing soliton solutions as well as lump solutions. With the assistance of this method one can transformed integrable equation into Hirota bilinear form under dependent variable transformation. Soliton solutions obtained by Hirota bilinear method are significant in mathematical physics, may be superimposed in fibers. These solitons are applicable in optical communications, which enable to produce faster, richer, more secure and more flexible communication systems. Also we will investigate the gravitational potential's behaviour on soliton solutions, such as parabolic, bright, dark, anti-dark, combination and S-shaped solitons. Contour plots and three-dimensional soliton solutions are provided. These solitons are important in nonlinear processes, magnetic devices, and lasers beams because of variations in gravitational field. [ABSTRACT FROM AUTHOR]

In this research, we study a variety of solutions like periodic, exponential, rational, hyperbolic and Jacobian elliptic function solutions of Rangwala–Rao equation (RRE) by employing complete discrimination system for polynomial (CDSP) technique. We deduce the relevant travelling wave system from the original equation using the travelling wave transformation and generate a conserved quantity, the Hamiltonian, from it. With the aid of qualitative theory of differential equation and bifurcation theory of planar dynamical systems a variety of phase portraits to the relevant travelling wave system of RRE are explored. The CDSP approach is not only useful for generating soliton solutions but also for carrying out qualitative analysis. Furthermore, 3D and 2D graphs are displayed for some of the soliton solutions of RRE. [ABSTRACT FROM AUTHOR]

In this manuscript, various types of breather, periodic cross-kink and rational solitons, M-shaped rational solutions with one and two kink and multi-waves will be discussed for Bose–Einstien condensate (BEC) model. We will compute the Kuznetsov–Ma breather, Akhmediev breather and generalized breather along with discussion on the interaction between them. At the end we will present the graphical description for our newly obtained solutions. [ABSTRACT FROM AUTHOR]

In this work, we utilize the extended simplest equation method to obtain exact solutions for the higher-order nonlinear Schrödinger's equation with fourth-order dispersion and cubic-quintic nonlinearity that describe the propagation of extremely short pulses in optical fibers. With the aid of this method, we get many exact solutions like singular-bright combo soliton solutions, bright, dark and singular soliton solutions, periodic solutions and other solutions. Moreover, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented. [ABSTRACT FROM AUTHOR]

In this paper, we will compute the conservation laws (CLs) of Chen–Lee–Liu equation (CLLE) with the help of scaling invariance technique. We will use Euler and Homotopy operators for the evaluation of conserved densities and fluxes. We will also obtain optical dromions with the help of Unified method (UM). By using this method, we will get domain walls, solitary wave and elliptic wave solutions. Moreover, we will investigate the stability as well as the integrability of the governing model by using linear stability technique and Painlevé analysis respectively. [ABSTRACT FROM AUTHOR]