Generation of Soliton Frequency Combs in NEMS.

In this study, we present an innovative approach leveraging combination internal resonances within a NEMS platform to generate mechanical soliton frequency combs (FCs) spanning a broad spectrum. In the time domain, the FCs take the form of a periodic train of narrow pulses, a highly coveted phenomenon within the realm of nonlinear wave-matter interactions. Our method relies on an intricate interaction among multiple vibration modes of a bracket-nanocantilever enabled by the strong nonlinearity of the electrostatic field. Through numerical simulation and experimental validation, we demonstrate that by amplifying the motions of the NEMS with the external electrostatic forcing tuned to excite the superharmonic resonance of order-n of the fundamental mode and exploiting combination internal resonances, we can generate multiple stable localized mechanical wave packets with different lobe sizes embodying soliton states I and II. This represents a significant breakthrough with profound implications for quantum computing and metrology.

Atomically Thin Current Pathways in Graphene through Kekulé-O Engineering.

We demonstrate that the current flow in graphene can be guided on atomically thin current pathways by the engineering of Kekulé-O distortions. A grain boundary in these distortions separates the system into topologically distinct regions and induces a ballistic domain-wall state. The state is independent of the orientation of the grain boundary with respect to the graphene sublattice and permits guiding the current on arbitrary paths. As the state is gapped, the current flow can be switched by electrostatic gates. Our findings are explained by a generalization of the Jackiw-Rebbi model, where the electrons behave in one region of the system as Fermions with an effective complex mass, making the device not only promising for technological applications but also a test-ground for concepts from high-energy physics. An atomic model supported by DFT calculations demonstrates that the system can be realized by decorating graphene with Ti atoms.

Ternary ReS2(1-x)Se2xalloys of different composition for Q-switched and mode-locked all-fiber laser.

This paper systematically studied the composition-controlled nonlinear optical properties and pulse modulation of ternary ReS2(1-x)Se2xalloys for the first time. The compositionally modulated characteristics of ReS2(1-x)Se2xon the band gap were simulated based on the first principles. We investigated the effect of the band gap on the saturable absorption properties. In addition, we demonstrated the modulation characteristics of different components ReS2(1-x)Se2xon 1.5µm Q-switched pulse performance. The Q-switched threshold, repetition rate, and pulse duration increase as the S(sulfur)-element composition rise. And pulse energy also was affected by the S(sulfur)-element composition. The ReS0.8Se1.2SA was selected to realize a conventional soliton with high energy in the all-fiber mode-locked laser. The pulse was centered at 1562.9 nm with a pulse duration of 2.26 ps, a repetition rate of 3.88 MHz, and maximum pulse energy of 1.95 nJ. This work suggests that ReS2(1-x)Se2xhas great potential in laser technology and nonlinear optics, and widely extends the material applications in ultrafast photonics.

Topological spin/structure couplings in layered chiral magnet Cr1/3TaS2: The discovery of spiral magnetic superstructure.

Chiral magnets have recently emerged as hosts for topological spin textures and related transport phenomena, which can find use in next-generation spintronic devices. The coupling between structural chirality and noncollinear magnetism is crucial for the stabilization of complex spin structures such as magnetic skyrmions. Most studies have been focused on the physical properties in homochiral states favored by crystal growth and the absence of long-ranged interactions between domains of opposite chirality. Therefore, effects of the high density of chiral domains and domain boundaries on magnetic states have been rarely explored so far. Herein, we report layered heterochiral Cr1/3TaS2, exhibiting numerous chiral domains forming topological defects and a nanometer-scale helimagnetic order interlocked with the structural chirality. Tuning the chiral domain density, we discovered a macroscopic topological magnetic texture inside each chiral domain that has an appearance of a spiral magnetic superstructure composed of quasiperiodic Néel domain walls. The spirality of this object can have either sign and is decoupled from the structural chirality. In weak, in-plane magnetic fields, it transforms into a nonspiral array of concentric ring domains. Numerical simulations suggest that this magnetic superstructure is stabilized by strains in the heterochiral state favoring noncollinear spins. Our results unveil topological structure/spin couplings in a wide range of different length scales and highly tunable spin textures in heterochiral magnets.

Observation and Characterization of Multiple Resonance Modes in a Chiral Helimagnet CrNb3S6.

The chiral helimagnet CrNb3S6 hosts various temperature- and magnetic-field-stabilized chiral soliton lattices (CSLs) and corresponding exotic collective spin resonance modes, which make it an ideal candidate for future magnetic storage/memory and magnon-based information processing. While most studies have focused on characterizing various static spin textures in this chiral helimagnet, its corresponding collective dynamics have rarely been explored. This study systematically investigates the temperature- and magnetic-field-dependent magnetic dynamics of a single crystal of CrNb3S6 using broadband microwave spectroscopy. We observe an optical mode with a temperature-independent mode number in addition to Kittel-like ferromagnetic resonance (FMR) modes in the CSL phase, consistent with the temperature-independent normalized CSL period L(H)/L(0) based on the 1D chiral sine-Gordon model. Furthermore, combining theoretical model fitting and micromagnetic simulation, we provide a detailed phase diagram and temporal-spatial resolution of dynamic modes, which may help to develop high-frequency exchange-coupling-based spintronic devices.

Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks.

In this paper, we apply a machine-learning approach to learn traveling solitary waves across various physical systems that are described by families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture, called Separable Gaussian Neural Networks (SGNN) into the framework of Physics-Informed Neural Networks (PINNs). Unlike the traditional PINNs that treat spatial and temporal data as independent inputs, the present method leverages wave characteristics to transform data into the so-called co-traveling wave frame. This reformulation effectively addresses the issue of propagation failure in PINNs when applied to large computational domains. Here, the SGNN architecture demonstrates robust approximation capabilities for single-peakon, multi-peakon, and stationary solutions (known as "leftons") within the (1+1)-dimensional, b-family of PDEs. In addition, we expand our investigations, and explore not only peakon solutions in the ab-family but also compacton solutions in (2+1)-dimensional, Rosenau-Hyman family of PDEs. A comparative analysis with multi-layer perceptron (MLP) reveals that SGNN achieves comparable accuracy with fewer than a tenth of the neurons, underscoring its efficiency and potential for broader application in solving complex nonlinear PDEs.

Cohomogeneity one solitons for the isometric flow of G 2 -structures.

We consider the existence of cohomogeneity one solitons for the isometric flow of G 2 -structures on the following classes of torsion-free G 2 -manifolds: the Euclidean R 7 with its standard G 2 -structure, metric cylinders over Calabi-Yau 3-folds, metric cones over nearly Kähler 6-manifolds, and the Bryant-Salamon G 2 -manifolds. In all cases we establish existence of global solutions to the isometric soliton equations, and determine the asymptotic behaviour of the torsion. In particular, existence of shrinking isometric solitons on R 7 is proved, giving support to the likely existence of type I singularities for the isometric flow. In each case, the study of the soliton equation reduces to a particular nonlinear ODE with a regular singular point, for which we provide a careful analysis. Finally, to simplify the derivation of the relevant equations in each case, we first establish several useful Riemannian geometric formulas for a general class of cohomogeneity one metrics on total spaces of vector bundles which should have much wider application, as such metrics arise often as explicit examples of special holonomy metrics.

Curvature-induced stabilization and field-driven dynamics of magnetic hopfions in toroidal nanorings.

Three dimensional magnetic textures are a cornerstone in magnetism research. In this work, we analyze the stabilization and dynamic response of a magnetic hopfion hosted in a toroidal nanoring with intrinsic Dzyaloshinskii-Moriya interaction simulating FeGe. Our results evidence that unlike their planar counterparts, where perpendicular magnetic anisotropies are necessary to stabilize hopfions, the shape anisotropy originated on the torus symmetry naturally yields the nucleation of these topological textures. We also analyze the magnetization dynamical response by applying a magnetic field pulse to differentiate among several magnetic patterns. Finally, to understand the nature of spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases and describe the differences among bulk and surface modes. Importantly, hopfions lying in toroidal nanorings present a non-circularly symmetric poloidal resonant mode, which is not observed in other systems hosting hopfions.

Electrically powered motions of toron crystallites in chiral liquid crystals.

Malleability of metals is an example of how the dynamics of defects like dislocations induced by external stresses alters material properties and enables technological applications. However, these defects move merely to comply with the mechanical forces applied on macroscopic scales, whereas the molecular and atomic building blocks behave like rigid particles. Here, we demonstrate how motions of crystallites and the defects between them can arise within the soft matter medium in an oscillating electric field applied to a chiral liquid crystal with polycrystalline quasi-hexagonal arrangements of self-assembled topological solitons called "torons." Periodic oscillations of electric field applied perpendicular to the plane of hexagonal lattices prompt repetitive shear-like deformations of the solitons, which synchronize the electrically powered self-shearing directions. The temporal evolution of deformations upon turning voltage on and off is not invariant upon reversal of time, prompting lateral translations of the crystallites of torons within quasi-hexagonal periodically deformed lattices. We probe how these motions depend on voltage and frequency of oscillating field applied in an experimental geometry resembling that of liquid crystal displays. We study the interrelations between synchronized deformations of the soft solitonic particles and their arrays, and the ensuing dynamics and giant number fluctuations mediated by motions of crystallites, five-seven defects pairs, and grain boundaries in the orderly organizations of solitons. We discuss how our findings may lead to technological and fundamental science applications of dynamic self-assemblies of topologically protected but highly deformable particle-like solitons.

A theory of mechanical stress-induced H2O2 signaling waveforms in Planta.

Recent progress in nanotechnology-enabled sensors that can be placed inside of living plants has shown that it is possible to relay and record real-time chemical signaling stimulated by various abiotic and biotic stresses. The mathematical form of the resulting local reactive oxygen species (ROS) wave released upon mechanical perturbation of plant leaves appears to be conserved across a large number of species, and produces a distinct waveform from other stresses including light, heat and pathogen-associated molecular pattern (PAMP)-induced stresses. Herein, we develop a quantitative theory of the local ROS signaling waveform resulting from mechanical stress in planta. We show that nonlinear, autocatalytic production and Fickian diffusion of H2O2 followed by first order decay well describes the spatial and temporal properties of the waveform. The reaction-diffusion system is analyzed in terms of a new approximate solution that we introduce for such problems based on a single term logistic function ansatz. The theory is able to describe experimental ROS waveforms and degradation dynamics such that species-dependent dimensionless wave velocities are revealed, corresponding to subtle changes in higher moments of the waveform through an apparently conserved signaling mechanism overall. This theory has utility in potentially decoding other stress signaling waveforms for light, heat and PAMP-induced stresses that are similarly under investigation. The approximate solution may also find use in applied agricultural sensing, facilitating the connection between measured waveform and plant physiology.

Directional soliton and breather beams.

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, solids, plasma, hydrodynamics, and optics.

Pattern Development and Control of Strained Solitons in Graphene Bilayers.

Engineering strain and interlayer registry in 2D crystals have been demonstrated as effective controls of their properties. Separation of domains with different interlayer registries in graphene bilayer has been reported, but the pattern control of strained solitons has not yet been achieved. We show here that, by pulling a graphene bilayer apart, soliton structures with a regularly modulated interlayer registry arise from the competition between elastic deformation in monolayers and local slip at the van der Waals interfaces. The commensurate-incommensurate transition with strain localization is identified as the interlayer overlap exceeds a critical size, where the continuum description of load transfer through the tension-shear chain breaks down. Birth, development and annihilation processes of the strained solitons can be controlled by the loading conditions. The effects of lattice symmetry and mechanical constraints are also discussed, completing the picture for microstructural evolution processes in the homo- or heterostructures of 2D crystals.

Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations.

Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins with a short overview of the literature connected to the methodology for obtaining exact solutions of nonlinear differential equations. This overview includes research on nonlinear waves, research on the methodology of the Inverse Scattering Transform method, and the method of Hirota, as well as some of the nonlinear equations studied by these methods. The overview continues with articles devoted to the phenomena described by the exact solutions of the nonlinear differential equations and articles about mathematical results connected to the methodology for obtaining such exact solutions. Several articles devoted to the numerical study of nonlinear waves are mentioned. Then, the approach to the SEsM is described starting from the Hopf-Cole transformation, the research of Kudryashov on the Method of the Simplest Equation, the approach to the Modified Method of the Simplest Equation, and the development of this methodology towards the SEsM. The description of the algorithm of the SEsM begins with the transformations that convert the nonlinearity of the solved complicated equation into a treatable kind of nonlinearity. Next, we discuss the use of composite functions in the steps of the algorithms. Special attention is given to the role of the simple equation in the SEsM. The connection of the methodology with other methods for obtaining exact multisoliton solutions of nonlinear differential equations is discussed. These methods are the Inverse Scattering Transform method and the Hirota method. Numerous examples of the application of the SEsM for obtaining exact solutions of nonlinear differential equations are demonstrated. One of the examples is connected to the exact solution of an equation that occurs in the SIR model of epidemic spreading. The solution of this equation can be used for modeling epidemic waves, for example, COVID-19 epidemic waves. Other examples of the application of the SEsM methodology are connected to the use of the differential equation of Bernoulli and Riccati as simple equations for obtaining exact solutions of more complicated nonlinear differential equations. The SEsM leads to a definition of a specific special function through a simple equation containing polynomial nonlinearities. The special function contains specific cases of numerous well-known functions such as the trigonometric and hyperbolic functions and the elliptic functions of Jacobi, Weierstrass, etc. Among the examples are the solutions of the differential equations of Fisher, equation of Burgers-Huxley, generalized equation of Camassa-Holm, generalized equation of Swift-Hohenberg, generalized Rayleigh equation, etc. Finally, we discuss the connection between the SEsM and the other methods for obtaining exact solutions of nonintegrable nonlinear differential equations. We present a conjecture about the relationship of the SEsM with these methods.

Solitonics with Polyacetylenes.

Polyacetylene molecular wires have attracted a long-standing interest for the past 40 years. From a fundamental perspective, there are two main reasons for the interest. First, polyacetylenes are a prime realization of a one-dimensional topological insulator. Second, long molecules support freely propagating topological domain-wall states, so-called "solitons," which provide an early paradigm for spin-charge separation. Because of recent experimental developments, individual polyacetylene chains can now be synthesized on substrates. Motivated by this breakthrough, we here propose a novel way for chemically supported soliton design in these systems. We demonstrate how to control the soliton position and how to read it out via external means. Also, we show how extra soliton-antisoliton pairs arise when applying a moderate static electric field. We thus make a step toward functionality of electronic devices based on soliton manipulation, that is, "solitonics".

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces.

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 µm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Nonlinear dynamics determines the thermodynamic instability of condensed matter in vacuo.

Condensed matter is thermodynamically unstable in a vacuum. That is what thermodynamics tells us through the relation showing that condensed matter at temperatures above absolute zero always has non-zero vapour pressure. This instability implies that at low temperatures energy must not be distributed equally among atoms in the crystal lattice but must be concentrated. In dynamical systems such concentrations of energy in localized excitations are well known in the form of discrete breathers, solitons and related nonlinear phenomena. It follows that to satisfy thermodynamics such localized excitations must exist in systems of condensed matter at arbitrarily low temperature and as such the nonlinear dynamics of condensed matter is crucial for its thermodynamics. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Collective excitations in α-helical protein structures interacting with the water environment.

Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic catalysis, intra-protein energy/charge transport, recognition, and allostery. To explain high effectiveness of these processes, two possible mechanisms of the long-lived excitation were proposed by H. Fröhlich and A.S. Davydov, which relate to either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with the aqueous environment. In the model, we distinguished three coupled subsystems, i.e., (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of the side-chain residuals which in turn interact with (iii) the environment, surrounding water responsible for dissipation and fluctuation in the system. It was shown that the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation which admits bifurcation into the solution corresponding to the weak-damped vibrational modes (Fröhlich-type regime) and Davydov solitons. A bifurcation parameter is derived through the strength of phonon-phonon interaction between the side-chains and hydration-shell water molecules. As shown, the energy of these excited states is pumped through the interaction of the side-chains with fluctuating water environment of the proteins. The suggested mechanism of the collective vibrational mode excitation is discussed in connection with the recent experiments on the long-lived collective protein excitations in the terahertz frequency region and vibrational energy transport pathways in proteins.

Solitions in magneto-optic waveguides with anti-cubic nonlinearity.

Optical soliton solutions are recovered for magneto-optic waveguides that maintains anti-cubic form of nonlinear refractive index. The analytical scheme is Jacobi's elliptic function approach. Once the solutions to the governing model are obtained in terms of Jacobi's elliptic functions, the limiting value to it's modulus of ellipticity reveals the complete spectrum of soliton solutions.

Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg-Landau Dynamical Equation with Applications and Stability.

In this paper, bright-dark, multi solitons, and other solutions of a (3 + 1)-dimensional cubic-quintic complex Ginzburg-Landau (CQCGL) dynamical equation are constructed via employing three proposed mathematical techniques. The propagation of ultrashort optical solitons in optical fiber is modeled by this equation. The complex Ginzburg-Landau equation with broken phase symmetry has strict positive space-time entropy for an open set of parameter values. The exact wave results in the forms of dark-bright solitons, breather-type solitons, multi solitons interaction, kink and anti-kink waves, solitary waves, periodic and trigonometric function solutions are achieved. These exact solutions have key applications in engineering and applied physics. The wave solutions that are constructed from existing techniques and novel structures of solitons can be obtained by giving the special values to parameters involved in these methods. The stability of this model is examined by employing the modulation instability analysis which confirms that the model is stable. The movements of some results are depicted graphically, which are constructive to researchers for understanding the complex phenomena of this model.

Monopole-antimonopole: interaction, scattering and creation.

The interaction of a magnetic monopole-antimonopole pair depends on their separation as well as on a second 'twist' degree of freedom. This novel interaction leads to a non-trivial bound state solution known as a sphaleron and to scattering in which the monopole-antimonopoles bounce off each other and do not annihilate. The twist degree of freedom also plays a role in numerical experiments in which gauge waves collide and create monopole-antimonopole pairs. Similar gauge wavepacket scatterings in the Abelian-Higgs model lead to the production of string loops that may be relevant to superconductors. Ongoing numerical experiments to study the production of electroweak sphalerons that result in changes in the Chern-Simons number, and hence baryon number, are also described but have not yet met with success. This article is part of a discussion meeting issue 'Topological avatars of new physics'.