Nonlinear Phenomena Research Articles

Decoherence in spin wave propagation via precursor pulses during signal equilibration

The processes for generation, amplification, and protraction of oscillating signals—often for information transfer—are inherently associated with dispersive decoherence and nonlinear phenomena. One such example is the case of wave patterns of non-negligible amplitudes that can emerge due to dispersion of a signal propagating through matter; for a continuously applied drive these patterns precede the main signal. Here, we investigate how spin wave generation inherently results in dispersive decoherence in the form of precursors. By quantifying three different frequency regimes, we investigate how decoherence is affected, or predetermined by the shape of the spin wave dispersion relation and, what is perhaps most interesting, it does not require non-linearity. Understanding the relationship between spin wave dispersion and decoherence can enable engineering magnonic devices supporting well-resolved signals for magnonic computing and signal processing.

Temporal and spatiotemporal soliton molecules in ultrafast fibre lasers

Abstract Ultrafast fibre lasers, characterized by ultrashort pulse duration and broad spectral bandwidth, have drawn significant attention due to their vast potential across a wide range of applications, from fundamental scientific to industrial processing and beyond. As dissipative nonlinear systems, ultrafast fibre lasers not only generate single solitons, but also exhibit various forms of spatiotemporal soliton bunching. Analogous to molecules composed of multiple atoms in chemistry, soliton molecules (SMs) – alias bound states – in ultrafast fibre lasers are a key concept for gaining a deeper understanding of nonlinear interaction and hold a promise for advancing high-capacity fibre-optic communications. SMs are particularly notable for their high degree of controllability, including their internal temporal separation, and relative phase differences, thereby suggesting new possibilities for manipulating multi-pulse systems. In this review, we provide a comprehensive overview of recent advancements in the studies of SMs with the multidimensional parameter space in ultrafast fibre lasers. Owing to the flexibility afforded by mode-locking techniques and dispersion management, various types of SMs – with diverse values of the soliton number, relative phase, pulse separation, carrier frequencies, and even modal dispersion – have been experimentally demonstrated. We also discuss other basic nonlinear optical phenomena observed in fibre lasers, including the formation, spatiotemporal pulsations, and interaction dynamics of SMs. Furthermore, we explore the multidimensional control of SMs through approaches such as gain modulation, polarization control, dispersion management, and photomechanical effects, along with their applications to optical data encoding. Finally, we discuss challenges and future development of multidimensional technologies for the manipulation of SMs.

The Nonlinear Dynamics and Chaos Control of Pricing Games in Group Robot Systems

System stability control in resource allocation is a critical issue in group robot systems. Against this backdrop, this study investigates the nonlinear dynamics and chaotic phenomena that arise during pricing games among finitely rational group robots and proposes control strategies to mitigate chaotic behaviors. A system model and a business model for group robots are developed based on market mechanism mapping, and the dynamics of resource allocation are formulated as a second-order discrete nonlinear system using game theory. Numerical simulations reveal that small perturbations in system parameters, such as pricing adjustment speed, product demand coefficients, and resource substitution coefficients, can induce chaotic behaviors. To address these chaotic phenomena, a control method combining state feedback and parameter adjustment is proposed. This approach dynamically tunes the state feedback intensity of the system via a control parameter M, thereby delaying bifurcations and suppressing chaotic behaviors. It ensures that the distribution of system eigenvalues satisfies stability conditions, allowing control over unstable periodic orbits and period-doubling bifurcations. Simulation results demonstrate that the proposed control method effectively delays period-doubling bifurcations and stabilizes unstable periodic orbits in chaotic attractors. The stability of the system’s Nash equilibrium is significantly improved, and the parameter range for equilibrium pricing is expanded. These findings provide essential theoretical foundations and practical guidance for the design and application of group robot systems.

Soliton dynamics and nonlinear wave theory: Understanding the interplay of thermal effects in plasma waves

The regularized long-wave ([Formula: see text]) equation is a fundamental model in shallow water wave theory, with extended relevance to other physical systems, such as plasma physics. The [Formula: see text] equation governs key nonlinear wave phenomena, including the propagation and interaction of solitons, or localized solitary waves. In plasma physics, it describes ion-acoustic waves, which are low-frequency compressional waves arising from the interaction between ions and electrons. While the ion-acoustic wave exhibits Korteweg–de Vries soliton behavior in the cold plasma limit, the [Formula: see text] equation offers a more accurate representation of ion-acoustic solitons and peaked structures in warm plasmas by accounting for thermal effects. This research presents novel analytical approximations for solitary wave solutions within the [Formula: see text] equation, which is critical for modeling nonlinear shallow water and plasma waves. The equation’s ability to describe peaked solitary waves, known as “peakons”, represents wave-breaking phenomena. By employing the improved Riccati expansion and modified Fan expansion techniques, this study derives periodic peakon solutions, offering new insights into the equation’s behavior. A thorough analysis of the [Formula: see text] equation is provided, emphasizing its importance for nonlinear wave modeling in both fluid and plasma systems. This paper also includes numerical validation using He’s variational iteration method, which enhances the transparency of the findings by addressing the underlying assumptions and limitations. The principal findings contribute to the broader understanding of nonlinear solitary wave theory, with practical implications for nonlinear wave dynamics across multiple physical domains. Suggested extensions are outlined for further investigation within this established theoretical framework. This study maintains consistent notation and terminology to facilitate clear communication of ideas in adherence to academic standards.

Dynamic behavior of solitons in nonlinear Schrödinger equations

The primary objective of this study is to derive analytical solutions for a significant system that models the evolution of complex wave fields in nonlinear media. This system extends the framework of nonlinear Schrödinger equations and is pivotal in various physical applications, including optical fibers and Bose-Einstein condensates. By employing advanced analytical techniques such as the Khater II, III (Khat II, Khat III) and Unified (UF) methods, we successfully obtain exact analytical solutions that enhance our understanding of the system’s dynamic behavior. The findings reveal a variety of soliton-like solutions, demonstrating the robustness and effectiveness of the methodologies employed. This research underscores the importance of the system in modeling intricate physical phenomena and offers a novel perspective on its solution space. The originality of this study lies in the innovative application of Khat II, Khat III, and UF methods to this system, providing valuable insights and methodologies for future research endeavors. This work represents a significant contribution to applied mathematics and nonlinear dynamics, emphasizing the physical relevance of the system in representing nonlinear wave interactions. The analytical solutions obtained can facilitate precise control and prediction of wave behaviors in practical applications, thereby advancing our capability to manipulate and harness nonlinear wave phenomena in diverse scientific and engineering contexts.

Corrigendum to “An elapsed time model for strongly coupled inhibitory and excitatory neural networks” [Physica D: Nonlinear Phenomena, 2021, vol. 425, p. 132977

Corrigendum to “An elapsed time model for strongly coupled inhibitory and excitatory neural networks” [Physica D: Nonlinear Phenomena, 2021, vol. 425, p. 132977

Investigating the nonlinear dynamics of acoustic waves by analyzing the Kadomtsev–Petviashvili equation in an unmagnetized plasma

This study explores the bifurcation analysis of ion-acoustic (IA) waves, electrostatic IA soliton propagation, as well as the behavior of periodic waves and chaos in a three-component, unmagnetized plasma composed of fully ionized ions and (r, q)-distributed electrons and positrons. To investigate the nonlinear behavior of IA waves across different plasma parameters, the Kadomtsev–Petviashvili equation is derived using the well-known reductive perturbation method. By applying a traveling wave transformation, a planar dynamical system is formulated. The phase portrait is then constructed to provide a detailed examination of the nonlinear wave phenomena emerging in the system. In addition, the Lyapunov spectrum is analyzed to determine whether the system exhibits chaotic motion. The impact of physical parameters on both the electrostatic and Sagdeev potentials is also studied. The findings of this research could contribute significantly to advancing the understanding of soliton propagation physics in astrophysical settings, various plasma environments, and laboratory experiments.

Electric field influence on the formation and evolution of vapor gas envelope in electrolytic plasma polishing

Electrolytic plasma polishing is an advanced technique for refining metal surfaces, particularly with intricate geometries, where the vapor-gas envelope (VGE) plays a crucial role in determining process efficiency and quality. Nonetheless, the nonlinear physics governing VGE dynamics, particularly the interactions between fluid dynamics, electrostrictive effects, and electric fields, remain inadequately explored. This research introduces a new mechanism for VGE evolution based on bubble deformation driven by nonlinear electric field interactions. A mathematical model derived from the Navier–Stokes equation, coupled with electrohydrodynamic forces, was developed to investigate VGE dynamics under varying voltage levels. Numerical simulations of electric field intensity, conductivity distribution, and pressure fields revealed the dominant role of electrostrictive forces in driving nanoscale vapor cavity deformation. The uneven electric forces generate mechanical stress, inducing nonlinear phenomena such as bubble contraction, coalescence, and expansion, further triggering nucleate boiling and film boiling. High-speed imaging of experiments using a linearly increasing voltage pulse validated the numerical results, showing how varying electric field strengths alter VGE formation, conductivity behavior, and temperature changes. At high field intensities (9 × 104 to 14 × 104 V/m), the balance between fluid dynamic pressure and electrostrictive forces stabilizes the VGE, forming negative pressure regions and enhanced bubble coalescence. Finally, the experimentally measured conductivity verifies the accuracy of the fluid model, and an empirical model of heat flow and temperature during the VGE process is established. The findings highlight the significance of electrostrictive forces in shaping VGE behavior and provide theoretical and practical insights for optimizing high-quality polishing processes.

Nonlinear Optical Bistability in a Bragg Reflector Multilayered Structure with MoS2

The special band structure of bilayer MoS2 makes it show strong nonlinear optical characteristics in the visible band, which provides a new way to develop visible nonlinear devices. In this paper, we present a theoretical analysis of the optical bistability (OB) in a silver–Bragg reflector structure by embedding bilayer MoS2 at the visible band. The nonlinear OB phenomenon is achieved due to the nonlinear conductivity of the bilayer MoS2 and the excitation of the optical Tamm state at the interface between the silver and the Bragg reflector. It is found that the hysteresis behavior and the threshold width of the OB can be effectively tuned by varying the incident light wavelength. In addition, the optical bistable behavior of the structure can be adjusted by varying the position of the MoS2 inset in the defect layer, the incident angle, and the structural parameters of the spacer layer. We believe the above results can provide a new paradigm for the construction of controllable bistable devices.

Coherent harmonic generation of magnons in spin textures

Harmonic generation, a notable non-linear phenomenon, has promising applications in information processing. For spin-waves in ferromagnetic materials, great progress has been made in the generation higher harmonics, however probing the coherence of these higher harmonics is challenging. Here, using in-situ diamond sensors, we study the coherent harmonic generation of spin waves in a soft ferromagnet. High-order resonance lines are generated via a microwave input and detected by nitrogen-vacancy (NV) centers in nanodiamonds. The phase coherence of the harmonic spin waves is verified by the Rabi oscillations of the NV electron spins. Numerical simulations indicate that the harmonic generation by microwaves below the ferromagnetic resonance frequency is associated with the nonlinear mixing of spin waves by magnetization structures at the film edge. Our finding of geometry-induced magnon harmonic generation constitutes a new way to generate magnon combs with coherent high-order harmonics and may pave the way for magnon-based information processing and quantum sensing applications.

Numerical investigation of sixth-order BDF compact difference scheme for viscous Burgers' equations

This paper explores and analyses the sixth-order backward differentiation formula (BDF6) compact difference scheme for solving the viscous Burgers' equation, which is used to describe the nonlinear phenomena in flow. First, the time derivative is discretized by virtue of the BDF6 approach. Subsequently, we employ a compact difference method, combined with an order reduction technique, to carry out spatial discretization, thereby establishing the fully discrete scheme. Then, for the existence and uniqueness of solutions to numerical scheme, a detailed theoretical analysis are carried out. Furthermore, by using discrete energy argument and mathematical induction, combined with several essential lemmas related to the BDF6 multiplier, we derive the convergence and stability in a novel way. Finally, the accuracy and effectiveness of the proposed scheme is validated through several numerical examples.

New soliton structure and trajectory equation for the asymmetrical Nizhnik- Novikov-Veselov equation with variable coefficients in incompressible fluid

Abstract This paper focuses on some new soliton structures and dynamic properties of the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation with variable coefficients, which can be used to describe the nonlinear wave phenomena in incompressible fluid, such as parameter regulation of soliton structures, hybridization behavior between different solitons and trajectory equations of soliton collisions. Firstly, the N-soliton solutions and parameter regulations are studied based on the bilinear form of equations. Secondly, the M-order lump solutions and trajectory equations are discussed by employing the long wave limit method. Finally, we focused on studying the interaction behavior between different solitons and the trajectory equations before and after collision, and provided a proof of the trajectory between the lump solution and the n-soliton before and after collision (where n is any positive integer).

Dynamics of multimode creeping solitons and soliton explosions in a spatiotemporal mode-locked laser

The study of high-dimensional solitons will bring great interest and new opportunities for understanding three-dimensional nonlinear physical phenomena and the design of complex nonlinear systems. The development of spatiotemporal mode-locked (STML) lasers has enabled the exploration of high-dimensional soliton dynamics. In this study, an STML laser and a dual-channel real-time measurement system based on dispersion Fourier transform technology were constructed. The real-time spectral evolution of high-dimensional solitons, including dissipative solitons, creeping solitons, and soliton explosions, are observed and studied. The experimental results show the complexity of multimode soliton dynamics. Such as multimode solitons possess the spectral-spatial characteristics that are absent in single-mode solitons, the transformations between steady-state solitons, creeping solitons, and soliton explosions, and the relationship between these transformations and pump energy changes and spatiotemporal saturated absorbers. To the best of our knowledge, this is also the first experimental report on multimode creeping solitons. This work provides insight into understanding complex spatiotemporal soliton dynamics and enriches the exploration of, to our knowledge, novel spatiotemporal dynamics.

Exploring Students' Perceptions and Experiences of Raising Concerns During Pre-Registration Training in England: A Systematic Review.

To explore the perceptions and experiences of students raising concerns during pre-registration health and/or social care training in England. Systematic review. MEDLINE, CINAHL, ERIC, PsycINFO and Education Research Complete were systematically searched for studies published between September 2015 and August 2024. Grey literature searches were conducted using Google Scholar and ETHOS British Library. Reference lists from included studies were hand searched. Joanna Briggs Institute methodological guidance for the conduct of systematic review informed conduct and the convergent integrated approach. Mixed methods appraisal tool was used for quality appraisal. Eleven studies were included. Synthesis of findings generated three themes: (1) conflicting needs of self and others, (2) navigating the professional workspace and, (3) 'choice to voice'. Speaking up and raising concerns as a pre-registration student is a complex, multi-faceted and non-linear social phenomenon. Experiences and perceptions are impacted by the novice student position alongside individual, interpersonal and organisational factors. Open cultures within teams and organisations, leadership, support and feedback may enable students overcome barriers to raising concerns. Raising concerns may reduce avoidable harm. Pre-registration students offer a 'fresh pair of eyes'; however, they face barriers related to their student position. Synthesis of speaking-up experiences and perceptions of students in English settings can inform the design of learning environments which equip pre-registration students with the knowledge and skills required to cultivate safety behaviours. These skills contribute positively to safety culture and support learning and improvement in complex systems such as health and social care. The review followed PRISMA reporting guidelines. The conceptualisation of this project was informed by engagement events with higher education staff, students and Freedom to Speak Up Guardians.

Vocal characteristics of distress and reproductive vocalizations in North American wapiti

Abstract Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes. Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evidence of biphonation and other nonlinear phenomena. Here, we analyse the acoustic structure of captive wapiti vocalizations to compare the male bugle with three categories of distress vocalizations: neonate distress (capture) calls, calf isolation calls, and adult female isolation calls. These four high-arousal call categories serve a common general function in recruiting conspecifics but occur in different behavioural contexts (capture, isolation, reproduction). Our goal was to distinguish characteristics that vary in graded steps that may correspond to an animal’s age or size from characteristics that are unique to the bugle. Characteristics of the high and loud fundamental (G0) varied in an age/size-graded manner with a decrease in minimum G0, an increase in the maximum and range of G0, with no evidence of sex differences. The nonlinear phenomena of deterministic chaos, biphonation, and frequency jumps were present in all four call categories and became more common from the distress vocalizations of neonates to calves to adult females to the male bugle. Two temporal characteristics sharply distinguished the bugle from the three categories of distress vocalizations: these included a prolonged call duration and a maximum G0 that occurred much later in the call for the bugle than for distress vocalizations. Our results suggest that distress vocalizations of different age groups and the reproductive bugle of wapiti share a high G0, with age/size-graded changes in G0 and nonlinear phenomena, but differ sharply in temporal characteristics.

Opportunities for gas-phase science at short-wavelength free-electron lasers with undulator-based polarization control

Free-electron lasers (FELs) are the world's most brilliant light sources with rapidly evolving technological capabilities in terms of ultrabright and ultrashort pulses over a large range of photon energies. Their revolutionary and innovative developments have opened new fields of science regarding nonlinear light-matter interaction, the investigation of ultrafast processes from specific observer sites, and approaches to imaging matter with atomic resolution. A core aspect of FEL science is the study of isolated and prototypical systems in the gas phase with the possibility of addressing well-defined electronic transitions or particular atomic sites in molecules. Notably for polarization-controlled short-wavelength FELs, the gas phase offers new avenues for investigations of nonlinear and ultrafast phenomena in spin-orientated systems, for decoding the function of the chiral building blocks of life as well as steering reactions and particle emission dynamics in otherwise inaccessible ways. This roadmap comprises descriptions of technological capabilities of facilities worldwide, innovative diagnostics and instrumentation, as well as recent scientific highlights, novel methodology, and mathematical modeling. The experimental and theoretical landscape of using polarization controllable FELs for dichroic light-matter interaction in the gas phase will be discussed and comprehensively outlined to stimulate and strengthen global collaborative efforts of all disciplines. Published by the American Physical Society 2025

Attosecond Rescattering of Laser-Assisted Electron-Proton Collision in Coulomb Potential.

This study investigates the motion of an electron in a Coulomb potential driven by an intense linearly polarized XUV laser pulse analyzed using Gordon-Volkov wave functions. The wave function is decomposed into spherical partial waves to model the scattered electron wave packet after the recollision with a proton. This interaction triggers high harmonic generation, producing coherent X-ray pulses with frequencies that are integer multiples of the XUV field. The research presents a novel method for achieving atomic-scale resolution at nanometer and subfemtosecond levels, enabling observation of electron-proton collisions on an attosecond time scale. It emphasizes the coupling of fields that create resonances in the scattered electron through photon energy exchange with XUV and X-ray pulses, leading to the formation of a Rydberg electron with energy levels up to n = 27 and angular momentum components l = 13 and m = ± 1. The combination of XUV and high-frequency X-ray fields introduces new nonperturbative nonlinear phenomena characterized by differential cross sections derived using the Floquet-Lippmann-Schwinger equation in the first-order Born approximation. The analysis shows that backward-forward scattering involves XUV-electron energy exchange, with peak intensity along the laser polarization vector, while sideways scattering, dominated by X-ray-electron interaction, peaks perpendicular to the polarization. Additionally, the laser-assisted scattering process results in temporary electron capture in a dressed proton-bound state, followed by escape and ejection, with the free electron ponderomotive energy exceeding 10Up.

Synthesis of a semimetallic Weyl ferromagnet with point Fermi surface.

Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moiré quantum matter and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall (QAH) effect1-3. By contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions4-6. Nearly all known Weyl materials are overwhelmingly metallic and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)2Te3. In transport, we find a record bulk anomalous Hall angle of greater than 0.5 along with non-metallic conductivity, a regime that is strongly distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation of more than 75% of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal-synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue towards new correlated states and nonlinear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices.

Correction: Nonlinear coexistence phenomenon and FPGA implementation with the hybrid of memristive–memcapacitive hyperchaotic system

Correction: Nonlinear coexistence phenomenon and FPGA implementation with the hybrid of memristive–memcapacitive hyperchaotic system

Adaptive Sampling Limit Surface Search Application to Identify Cliff-Edge Effects in Severe Accident Uncertainty Analysis

Severe accident (SA) codes and their core degradation models have to deal with strongly nonlinear and discontinuous phenomena. In the application of uncertainty quantification to SA simulations, the combination of such phenomena may lead to a strong increase in the uncertainty propagated through the simulation, as well as to the chaotic behavior of the output variables. In this framework, the application of the limit surface search method of the RAVEN tool is proposed for a case where cliff-edge effects of SA phenomena determine a bifurcation of an output figure of merit. The algorithm is based on a predictive method making use of a support vector machine model, and it is applied with the aim of separating those input values that lead to different phenomenologies among the uncertainty calculations. The case study is in regard to the uncertainty analysis of the ASTEC code simulation of the QUENCH6 experimental test conducted in the framework of the International Atomic Energy Agency Coordinated Research Project I31033.