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.

Regularity and wave study of an advection-diffusion-reaction equation.

In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended direct algebraic method with traveling wave transformation has been used. Achieved soliton solutions are different functions which are hyperbolic, trigonometric, exponential, and some mixed trigonometric functions. These functions show the nature of solitons. Two and three-dimensional plots are drawn using different values of parameters and coefficients for the comparison and behavior of solitons as combined bright-dark, dark, and bright solitons.

Novel soliton solutions and phase plane analysis in nonlinear Schrödinger equations with logarithmic nonlinearities.

This paper investigates a generalized form of the nonlinear Schrödinger equation characterized by a logarithmic nonlinearity. The nonlinear Schrödinger equation, a fundamental equation in nonlinear wave theory, is applied across various physical systems including nonlinear optics, Bose-Einstein condensates, and fluid dynamics. We specifically explore a logarithmic variant of the nonlinear Schrödinger equation to model complex wave phenomena that conventional polynomial nonlinearities fail to capture. We derive four distinct forms of the nonlinear Schrödinger equation with logarithmic nonlinearity and provide exact solutions for each, encompassing bright, dark, and kink-type solitons, as well as a range of periodic solitary waves. Analytical techniques are employed to construct bounded and unbounded traveling wave solutions, and the dynamics of these solutions are analyzed through phase portraits of the associated dynamical systems. These findings extend the scope of the nonlinear Schrödinger equation to more accurately describe wave behaviors in complex media and open avenues for future research into non-standard nonlinear wave equations.

Interactions among lump optical solitons for coupled nonlinear Schrödinger equation with variable coefficient via bilinear method.

In this paper, a non-autonomous (3+1) dimensional coupled nonlinear Schrödinger equation (NLSE) with variable coefficients in optical fiber communication is analyzed. By means of bilinear technique and symbolic computations, new multi-soliton solutions of the coupled model in different trigonometric and lump functions are given. Then, in terms of perturbed waves, considering the steady state solution and the small perturbation on the three directions x, y, z and the time t, the soliton transmission are also considered. The behaviour of interaction among lump periodic soliton is studied and optical soliton solutions are reached. This study has certain significance for the analysis of other nonlinear dispersion systems and the application of optical physics. The results are presented through graphs generated by using Maple. The important feature of the proposed study is to show different behaviour of the soliton at each component. The behaviour of solitons, their interactions, and their transformations are all governed by the fundamental concept of energy conservation in all three examples. We demonstrate the efficiency of our suggested methodology for analyzing the NLSE equations using the numerical simulations and analytical tools, yielding fresh insights into their behaviour and solutions. Our findings help to develop mathematical tools for investigating nonlinear partial differential equation (NLPDEs) and provide new insights on the dynamics of NLSE equations, which have implications for many domains of physics and applied mathematics.

Analysis of fractional solitary wave propagation with parametric effects and qualitative analysis of the modified Korteweg-de Vries-Kadomtsev-Petviashvili equation.

This study explores the fractional form of modified Korteweg-de Vries-Kadomtsev-Petviashvili equation. This equation offers the physical description of how waves propagate and explains how nonlinearity and dispersion may lead to complex and fascinating wave phenomena arising in the diversity of fields like optical fibers, fluid dynamics, plasma waves, and shallow water waves. A variety of solutions in different shapes like bright, dark, singular, and combo solitary wave solutions have been extracted. Two recently developed integration tools known as generalized Arnous method and enhanced modified extended tanh-expansion method have been applied to secure the wave structures. Moreover, the physical significance of obtained solutions is meticulously analyzed by presenting a variety of graphs that illustrate the behaviour of the solutions for specific parameter values and a comprehensive investigation into the influence of the nonlinear parameter on the propagation of the solitary wave have been observed. Further, the governing equation is discussed for the qualitative analysis by the assistance of the Galilean transformation. Chaotic behavior is investigated by introducing a perturbed term in the dynamical system and presenting various analyses, including Poincare maps, time series, 2-dimensional 3-dimensional phase portraits. Moreover, chaotic attractor and sensitivity analysis are also observed. Our findings affirm the reliability of the applied techniques and suggest its potential application in future endeavours to uncover diverse and novel soliton solutions for other nonlinear evolution equations encountered in the realms of mathematical physics and engineering.

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.

Analysis of multi-wave solitary solutions of (2+1)-dimensional coupled system of Boiti-Leon-Pempinelli.

This work examines the (2+1)-dimensional Boiti-Leon-Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti-Leon-Pempinelli equation by applying the Sardar sub-equation technique. This method is shown to be a reliable and practical tool for solving nonlinear wave equations. Furthermore, different types of solitary wave solutions are constructed: w-shaped, breather waved, chirped, dark, bright, kink, unique, periodic, and more. The results obtained with the variable coefficient Boiti-Leon-Pempinelli equation are stable and different from previous methods. As compared to their constant-coefficient counterparts, the variable-coefficient models are more general here. In the current work, the problem is solved using the Sardar Sub-problem Technique to produce distinct soliton solutions with parameters. Plotting these graphs of the solutions will help you better comprehend the model. The outcomes demonstrate how well the method works to solve nonlinear partial differential equations, which are common in mathematical physics.With the help of this method, we may examine a variety of solutions from significant physical perspectives.

Investigating pseudo parabolic dynamics through phase portraits, sensitivity, chaos and soliton behavior.

This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system's behavior and the extent to which it deviates from the unperturbed case.

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.

Photorefraction Simulates Well the Plasticity of Neural Synaptic Connections.

In recent years, the need for systems capable of achieving the dynamic learning and information storage efficiency of the biological brain has led to the emergence of neuromorphic research. In particular, neuromorphic optics was born with the idea of reproducing the functional and structural properties of the biological brain. In this context, solitonic neuromorphic research has demonstrated the ability to reproduce dynamic and plastic structures capable of learning and storing through conformational changes in the network. In this paper, we demonstrate that solitonic neural networks are capable of mimicking the functional behaviour of biological neural tissue, in terms of synaptic formation procedures and dynamic reinforcement.

Dual Role of Beam Polarization and Power in Nematic Liquid Crystals: A Comprehensive Study of TE- and TM-Beam Interactions.

Optical spatial solitons are self-guided wave packets that maintain their transverse profile due to the self-focusing effect of light. In nematic liquid crystals (NLC), such light beams, called nematicons, can be induced by two principal mechanisms: light-induced reorientation of the elongated molecules and thermal changes in the refractive index caused by partial light absorption. This paper presents a detailed investigation of the propagation dynamics of light beams in nematic liquid crystals (NLCs) doped with Sudan Blue dye. Building on the foundational understanding of reorientational and thermal solitons in NLCs and the effective breaking of the action-reaction principle in spatial solitons, this study examines the interaction of infrared (IR) and visible beams in a [-4-(trans-4'-exylcyclohexyl)isothiocyanatobenzene] (6CHBT) NLC. Our experimental results highlight the intricate interplay of beam polarizations, power levels, and the nonlinear properties of NLCs, offering new insights into photonics and nonlinear optics in liquid crystals.

Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas.

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail.

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.

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.

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach.

The analytical soliton solutions place a lot of value on birefringent fibres. The major goal of this study is to generate novel forms of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which depicts unstable optical solitons that arise from optical propagations using birefringent fibres. The (presumably new) extended direct algebraic (EDA) technique is used here to extract a large number of solutions for RKLE. It gives soliton solutions up to thirty-seven, which essentially correspond to all soliton families. This method's ability to determine many sorts of solutions through a single process is one of its key advantages. Additionally, it is simple to infer that the technique employed in this study is really straightforward yet one of the quite effective approaches to solving nonlinear partial differential equations so, this novel extended direct algebraic (EDA) technique may be regarded as a comprehensive procedure. The resulting solutions are found to be hyperbolic, periodic, trigonometric, bright and dark, combined bright-dark, and W-shaped soliton, and these solutions are visually represented by means of 2D, 3D, and density plots. The present study can be extended to investigate several other nonlinear systems to understand the physical insights of the optical propagations through birefringent fibre.

Surpassing the nonlinear conversion efficiency of soliton microcombs.

Laser frequency combs are enabling some of the most exciting scientific endeavours in the twenty-first century, ranging from the development of optical clocks to the calibration of the astronomical spectrographs used for discovering Earth-like exoplanets. Dissipative Kerr solitons generated in microresonators currently offer the prospect of attaining frequency combs in miniaturized systems by capitalizing on advances in photonic integration. Most of the applications based on soliton microcombs rely on tuning a continuous-wave laser into a longitudinal mode of a microresonator engineered to display anomalous dispersion. In this configuration, however, nonlinear physics precludes one from attaining dissipative Kerr solitons with high power conversion efficiency, with typical comb powers amounting to ~1% of the available laser power. Here we demonstrate that this fundamental limitation can be overcome by inducing a controllable frequency shift to a selected cavity resonance. Experimentally, we realize this shift using two linearly coupled anomalous-dispersion microresonators, resulting in a coherent dissipative Kerr soliton with a conversion efficiency exceeding 50% and excellent line spacing stability. We describe the soliton dynamics in this configuration and find vastly modified characteristics. By optimizing the microcomb power available on-chip, these results facilitate the practical implementation of a scalable integrated photonic architecture for energy-efficient applications.

Exact chirped solutions of perturbed Chen-Lee-Liu equation with refractive index.

We study the exact chirped solutions of the perturbed Chen-Lee-Liu equation with a refractive index. Exact chirped solutions and their corresponding chirps are obtained using trial equation method and complete discrimination system for polynomial. Illustrations are presented under certain parameter conditions. Chen-Lee-Liu model describes pulse propagation in optical fibers. Studying chirped solutions to the perturbed Chen-Lee-Liu equation with a refractive index could improve the understanding of physical phenomena and may have applications in the design of optical fibers.

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.

Observation of π solitons in oscillating waveguide arrays.

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.

Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain.

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials. This study investigates a new type of moiré superlattice in bilayer graphene when one layer is biaxially strained with respect to the other-so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moiré engineering in van der Waals multilayers.