Nonlinear Physics Research Articles

Shockwavelike Behavior across Social Media.

Online communities featuring "anti-X" hate and extremism, somehow thrive online despite moderator pressure. We present a first-principles theory of their dynamics, which accounts for the fact that the online population comprises diverse individuals and evolves in time. The resulting equation represents a novel generalization of nonlinear fluid physics and explains the observed behavior across scales. Its shockwavelike solutions explain how, why, and when such activity rises from "out-of-nowhere," and show how it can be delayed, reshaped, and even prevented by adjusting the online collective chemistry. This theory and findings should also be applicable to anti-X activity in next-generation ecosystems featuring blockchain platforms and Metaverses.

Exploration of New Solitons for the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model

The key objective of the current manuscript was to investigate the exact solutions of the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. For this purpose, we applied two reliable and efficient approaches; specifically, the modified simple equation (MSE) and exponential rational function (ERF) techniques. The methods considered in this paper offer solutions for problems in nonlinear theory and mathematical physics practice. We also present solutions obtained graphically with the Maple package program.

A review on the fluid structure interaction of circular plates using numerical methods

Fluid structure interaction is a nonlinear multi physics phenomenon that have wide range of applications in science and engineering fields. This article presents the development of numerical methods to solve the fluid structure interaction problem deals with the vibration analysis of plate structures in contact with fluid. The modeling of fluid and structure are essential to study the fluid structure interaction problems. The development of suitable mathematical models and their validation are discussed herewith.

Multiple fusion solutions and other waves behavior to the Broer-Kaup-Kupershmidt system

In this article, the Hirota bilinear method is utilized to reveal multi-fusion solutions to the Broer-Kaup-Kupershmidt (BKK) system in (2 + 1)-dimension. The Broer-Kaup equations are a pair of linked nonlinear partial differential equations which plays a great role in nonlinear physics. The solutions are one-, two-, three-, and four-soliton resonant wave solutions. On the other hand, the new modified Sardar sub-equation method (SSEM) is employed to reach complex wave solutions in the form of topological, non-topological, and other wave solutions. By selecting suitable values for parameters, the dynamics of some of the reported solutions are graphed. The reported solutions are novel and have not previously been reported in the present literature. The solutions may be useful in explaining the physical meaning of various nonlinear physical models.

Argonda Dairesel Polarize Yüksek Harmonikler: Dipol ve Dipol Olmayan Etki

The interaction of the intense laser pulse, which forms the basis of the strong laser field and non-linear optical physics, with atoms, molecules, and solids leads to the High Order Harmonic Generation (HHG). There are many theoretical and experimental research related to this process defined by the Semi-Classic Model which is called the Three Step Model. In this article, the dipole and non-dipole effects specified in the theoretical Lewenstein model to be used in the Argon atom interacting with the strong circular laser field (800nm) and the resulting higher order harmonic spectrum will be investigated. We compared the results obtained using the non-collinear beams with opposite circular polarizations with those obtained using a single circularly polarized beam or a linearly polarized beam. It could be said that the circular polarization can significantly affect the HHG process in an argon atom exposed to a laser field with 800 nm wavelength and 1015 W/cm2 intensity.

Kink and breather waves with and without singular solutions to the Zoomeron model

The Zoomeron model is applied to various types of solitons arising in fluid mechanics, laser optics, and nonlinear physics. We derive analytical solutions to the mentioned model using the exp(−λ(ς))-expansion, the generalized Kudryashov, and the generalized tanh schemes. We obtain the kink waves, breather waves, bright soliton, and dark soliton of this model via symbolic computation. We also get both singular kink waves and singular breather waves. The dynamics of the adopted results are shown in density and 3D graphics. The obtained outcomes will play a vital role in further studies of complicated nonlinear models.

Berry curvature dipole and nonlinear Hall effect in two-dimensional Nb2n+1SinTe4n+2

Recent experiments have demonstrated interesting physics in a family of two-dimensional composition-tunable materials ${\mathrm{Nb}}_{2n+1}{\mathrm{Si}}_{n}{\mathrm{Te}}_{4n+2}$. Here we show that, owing to their intrinsic low symmetry, metallic nature, tunable composition, and ambient stability, these materials offer a good platform for studying the Berry curvature dipole (BCD) and nonlinear Hall effect. Using first-principles calculations, we find that the BCD exhibits pronounced peaks in monolayer ${\mathrm{Nb}}_{3}{\mathrm{SiTe}}_{6}$ (the $n=1$ case). Its magnitude decreases monotonically with $n$ and completely vanishes in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. This variation manifests a special hidden dimensional crossover of the low-energy electronic states in this system. The resulting nonlinear Hall response from the BCD in these materials is discussed. Our work reveals pronounced geometric quantities and nonlinear transport physics in ${\mathrm{Nb}}_{2n+1}{\mathrm{Si}}_{n}{\mathrm{Te}}_{4n+2}$ family materials, which should be readily detected in experiment.

Geospatial visualization of indicators for the dynamics of innovation in an educational institution applying clustering techniques

The activities of science, technology, and innovation are related to the execution of actions involving research, experimental development, support for education and training, provision of scientific and technological services, administration, and other management activities. In this context, the SENNOVA Research System of Servicio Nacional de Aprendizaje of Colombia dedicates human and technological resources to contribute to the country’s economic and social growth, looking to answer the need to develop Colombia’s productive sector. In turn, these contributions also generate social dynamics in which the activity at the institutional level can be represented as a kind of the complex systems studied by nonlinear Physics. These complex dynamics are suitable for visualization from the stochastic processes that lead to statistical distributions typical of complex systems. A data analytics model for the measurement and visualization of innovation indicators is being developed in the Antioquia regional branch of Servicio Nacional de Aprendizaje, where the distinct categories of science, technology, and innovation activities are graphically identified to facilitate the analysis of the results obtained from both descriptive statistics and data science. From the perspective of complex systems for representing these institutional social dynamics, clustering processes with techniques such as K-means grouping were implemented. Potential distributions determined by the conglomerates of management processes and productivity of the projects executed in the analyzed institution over a given period are identified as innovation indicators and subsequently classified using principal component analysis. Python Folium was used as a visualization tool to graphically generate comparisons between the different Servicio Nacional de Aprendizaje centers of the Antioquia regional branch in each period. The results show greater ease of interpretation and analysis of statistical results and data analytics in measuring indicators of science, technology, and innovation activities through the techniques employed in comparison with traditional data visualization tools.

Amplification of a terahertz wave via stimulated Raman scattering.

Extremely strong terahertz (THz) waves are desperately demanded for investigating nonlinear physics, spectroscopy, and imaging in the THz range. However, traditional crystal-/semiconductor-based THz sources have limitations of reaching extremely high amplitude due to the damage threshold of devices. Here, by introducing Raman amplification to the THz range, we propose a novel, to the best of our knowledge, scheme to amplify THz waves in plasma. A long-pulse CO2 pump laser transfers its energy to a multicycle, 10-THz seed in a two-step plasma. By one-dimensional simulations, a 0.87-GV/m, 1.2-ps-duration THz seed is amplified to 10 GV/m in a 5.7-mm-long plasma with an amplification efficiency approaching 1%. The method provides a new technology to manipulate the intensity of THz waves.

Dynamics on novel wave structures of non-linear Schrödinger equation via extended hyperbolic function method

In this study, our focus is on the construction of novel soliton solutions of non-linear Schrödinger equation with parabolic law and non-local law non-linearities via new extended hyperbolic function method. The acquired solutions are original and could be helpful in the field of nonlinear optics, fluid dynamics, and plasma physics. From these outcomes, it is believed that this method is a promising technique to handle a wide variety of such type of equations. For physical understanding and better realization of our constructed solutions, some of the obtained solutions under appropriate parameters are demonstrated by 2D and 3D plots. Analysis discloses that the proposed scheme is consistent and can be applied to more advanced models in engineering and physics.

Soliton Microcombs Multiplexing Using Intracavity-Stimulated Brillouin Lasers.

Solitons in microresonators have spurred intriguing nonlinear optical physics and photonic applications. Here, by combining Kerr and Brillouin nonlinearities in an over-modal microcavity, we demonstrate spatial multiplexing of soliton microcombs under a single external laser pumping operation. This demonstration offers an ideal scheme to realize highly coherent dual-comb sources in a compact, low-cost and energy-efficient manner, with uniquely low beating noise. Moreover, by selecting the dual-comb modes, the repetition rate difference of a dual-comb pair could be flexibly switched, ranging from 8.5 to 212MHz. Beyond dual-comb, the high-density mode geometry allows the cascaded Brillouin lasers, driving the co-generation of up to 5 space-multiplexing frequency combs in distinct mode families. This Letter offers a novel physics paradigm for comb interferometry and provides a widely appropriate tool for versatile applications such as comb metrology, spectroscopy, and ranging.

Resonant collisions of high-order localized waves in the Maccari system

Exploring new nonlinear wave solutions to integrable systems has always been an open issue in physics, applied mathematics, and engineering. In this paper, the Maccari system, a two-dimensional analog of nonlinear Schrödinger equation, is investigated. The system is derived from the Kadomtsev–Petviashvili (KP) equation and is widely used in nonlinear optics, plasma physics, and water waves. A large family of semi-rational solutions of the Maccari system are proposed with the KP hierarchy reduction method and Hirota bilinear method. These semi-rational solutions reduce to the breathers of elastic collision and resonant collision under special parameters. In case of resonant collisions between breathers and rational waves, these semi-rational solutions describe lumps fusion into breathers, or lumps fission from breathers, or a mixture of these fusion and fission. The resonant collisions of semi-rational solutions are semi-localized in time (i.e., lumps exist only when t → +∞ or t → −∞), and we also discuss their dynamics and asymptotic behaviors.

Time-dependent saturation and physics-based nonlinear model of cross-beam energy transfer

The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.

Plenty of accurate novel solitary wave solutions of the fractional Chaffee–Infante equation

This work focuses on the accuracy and numerical strategies for solving the fractional Chaffee–Infante (CIE) equation in (2+1) dimensions computationally. This model illustrates the flow and transformation of gas as it travels through a homogeneous medium. When the constituents of a medium do not alter from their initial state, we say that the medium is homogeneous. In none of the solutions did we change the proportions of the individual components. Three novel analytical and numerical techniques provide new, dependable approaches for determining and estimating responses. The tabular data shown here facilitates interpreting the numerical data presented below. The simulations, which are exhibited in both 2D and 3D, depict the behavior of a solitary solitaire in both the natural and digital worlds. These findings demonstrate that this strategy is the most effective way to solve nonlinear mathematical physics problems.

On the intrinsic pinning and shape of charge-density waves in 1D Peierls systems

Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of the electron-lattice models in the physical properties of Peierls systems? We study in details a nonlinear discrete model, introduced by Brazovskii, Dzyaloshinskii and Krichever. First, we recall its exact analytical solution at integrable points. It is a cnoidal wave, with a continuous envelope, which may slide over the lattice potential at no energy cost, following Fröhlich’s argument. Second, we show numerically that integrability-breaking terms modify some important physical properties. The envelope function may become discontinuous: electrons form stronger chemical bonds which are local dimers or oligomers. We show that an Aubry transition from the sliding phase to an insulating pinned phase occurs when the model is no longer integrable.

Novel waves structures for two nonlinear partial differential equations arising in the nonlinear optics via Sardar-subequation method

In this paper, our aim is to construct the novel wave structures for two non-linear evolution equations which are rising in non-linear optics, mathematical biological models, fluid dynamics, waves theory, mechanics, quantum mechanics, and many more. We employed an efficient analytical technique namely, the Sardar-subequation method to build the wave solutions for the modified Benjamin-Bona-Mahony equation and the Coupled Klein–Gordon equations. We have built the numerous type of soliton wave structures of modified Benjamin-Bona-Mahony equation and the Coupled Klein–Gordon equations via the Sardar-subequation method. Acquired results reveal the dynamics behavior of waves structures including the bright, singular, dark, and periodic singular solitons solutions. To illustrate the behavior of these solutions some selected solutions are sketched in two-, and three-dimensional graphs. On the basis of these results, our technique is suitable, up-to-date, and powerful. The obtained solutions are very efficacious and influential in non-linear optics, mathematical biology, mechanics, fluid mechanics, plasma physics, and many more. This study will assist to predict some new hypothesis and theories in the field of mathematical physics.

Bifurcation, sensitivity analysis and exact traveling wave solutions for the stochastic fractional Hirota–Maccari system

The stochastic fraction Hirota–Maccari system is used as a governing model to check the wave propagation in nonlinear optics, plasma physics and hydrodynamics. Firstly, the random fractional order Hirota–Maccari system is transformed into a two-dimensional plane dynamic system by using traveling wave transformation. Secondly, the bifurcation is discussed by using the theory of plane dynamic system, and the sensitivity to the strength and frequency of perturbation is analyzed. In addition, the exact traveling wave solution of the stochastic fractional Hirota–Maccari system is constructed by using the analytical method of the plane dynamic system. Finally, the results of comparison analysis indicated that the fractional derivatives and noises will greatly influence the solution behavior.

Two-Dimensional Gap Solitons in Parity-Time Symmetry Moiré Optical Lattices with Rydberg–Rydberg Interaction

Realizing single light solitons that are stable in high dimensions is a long-standing goal in research of nonlinear optical physics. Here, we address a scheme to generate stable two-dimensional solitons in a cold Rydberg atomic system with a parity-time (PT) symmetric moiré optical lattice. We uncover the formation, properties, and their dynamics of fundamental and two-pole gap solitons as well as vortical ones. The PT symmetry, lattice strength, and the degrees of local and nonlocal nonlinearity are tunable and can be used to control solitons. The stability regions of these solitons are evaluated in two numerical ways: linear-stability analysis and time evolutions with perturbations. Our results provide an insightful understanding of solitons physics in combined versatile platforms of PT-symmetric systems and Rydberg–Rydberg interaction in cold gases.

Dual-mode nonlinear Schrödinger equation (DMNLSE): Lie group analysis, group invariant solutions, and conservation laws

This paper proposed a novel dual-mode nonlinear Schrödinger equation (DMNLSE) with cubic law. The DMNLSE describes the propagations of two moving waves simultaneously. This nonlinear Schrödinger equation (NLSE) model appears in different areas of physics, including nonlinear optics, plasma physics, superconductivity, and quantum mechanics. In the context of photonics, NLSE models the propagation of soliton pulses through inter-continental distances. In this study, the Lie symmetry procedure is successfully utilized on the DMNLSE to discover the infinitesimal generators using the invariance condition. Then, we transform the DMNLSE into an ordinary differential equation (ODE) employing accepted generators and similarity reduction concepts. Later, we consider conservation laws for the DMNLSE. Thanks to the multiplier technique, the conserved quantities’ densities and fluxes are discovered. With the aid of the Mathematica package program, 3D, contour, and density graphs were drawn for the special values of the parameters in the solutions, and the physical structures of the solutions obtained in this way were also observed.

A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions

Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This paper aims to extend the classic lower-dimensional integrable models to arbitrary spatial dimension. We investigate the celebrated Kadomtsev–Petviashvili (KP) equation and propose its (n+1)-dimensional integrable extension. Based on the singularity manifold analysis and binary Bell polynomial method, it is found that the (n+1)-dimensional generalized KP equation has N-soliton solutions, and it also possesses the Painlevé property, Lax pair, Bäcklund transformation as well as infinite conservation laws, and thus the (n+1)-dimensional generalized KP equation is proven to be completely integrable. Moreover, various types of localized solutions can be constructed starting from the N-soliton solutions. The abundant interactions including overtaking solitons, head-on solitons, one-order lump, two-order lump, breather, breather-soliton mixed solutions are analyzed by some graphs.