Soliton Configurations Research Articles

New Coupled Optical Solitons to Birefringent Fibers for Complex Ginzburg–Landau Equations with Hamiltonian Perturbations and Kerr Law Nonlinearity

In this study, we use an analytical method tailored for the in-depth exploration of coupled nonlinear partial differential equations (NLPDEs), with a primary focus on the dynamics of solitons. Traditional methods are quite effective for solving individual nonlinear partial differential equations (NLPDEs). However, their performance diminishes notably when addressing systems of coupled NLPDEs. This decline in effectiveness is mainly due to the complex interaction terms that arise in these coupled systems. Commonly, researchers have attempted to simplify coupled NLPDEs into single equations by imposing proportional relationships between various solutions. Unfortunately, this simplification often leads to a significant deviation from the true physical phenomena that these equations aim to describe. Our approach is distinctively advantageous in its straightforwardness and precision, offering a clearer and more insightful analytical perspective for examining coupled NLPDEs. It is capable of concurrently facilitating the propagation of different soliton types in two distinct systems through a single process. It also supports the spontaneous emergence of similar solitons in both systems with minimal restrictions. It has been extensively used to investigate a wide array of new coupled progressive solitons in birefringent fibers, specifically for complex Ginzburg–Landau Equations (CGLEs) involving Hamiltonian perturbations and Kerr law nonlinearity. The resulting solitons, with comprehensive 2D and 3D visualizations, showcase a variety of coupled soliton configurations, including several that are unprecedented in the field. This innovative approach not only addresses a significant gap in existing methodologies but also broadens the horizons for future research in optical communications and related disciplines.

Supersymmetric smooth distributions of M2-branes as AdS solitons

We show that the singularities of certain distributions of M2-branes can be removed by adding a Wilson loop around a compact direction along the brane. The holographic coordinate naturally ends up before the singularity and the resulting spacetime provides an AdS soliton configuration, albeit possibly supersymmetric. We study the phase space diagram of these M2-branes distributions endowed with Wilson loops and show that different distributions are interconnected, providing a rich structure of phase transitions at zero temperature.

Condensation and evaporation of boson stars

Axion-like particles, including the QCD axion, are well-motivated dark matter candidates. Numerical simulations have revealed coherent soliton configurations, also known as boson stars, in the centers of axion halos. We study evolution of axion solitons immersed into a gas of axion waves with Maxwellian velocity distribution. Combining analytical approach with controlled numerical simulations we find that heavy solitons grow by condensation of axions from the gas, while light solitons evaporate. We deduce the parametric dependence of the soliton growth/evaporation rate and show that it is proportional to the rate of the kinetic relaxation in the gas. The proportionality coefficient is controlled by the product of the soliton radius and the typical gas momentum or, equivalently, the ratio of the gas and soliton virial temperatures. We discuss the asymptotics of the rate when this parameter is large or small.

Q -balls in the sky

There may exist extended configurations in the dark matter sector that are analogs of structures in the visible sector. In this work, we explore nontopological solitonic configurations, specifically Q-balls, and study when they may form macroscopic astrophysical structures and what their distinct characteristics might be. We study in some detail theoretical bounds on their sizes and constraints on the underlying parameters, based on criteria for an astrophysical Q-ball’s existence, gravitational stability and viability of solutions. Following this path, one is able to obtain novel limits on astrophysical Q-ball sizes and their underlying parameters. We also explore the gravitational lensing features of different astrophysical Q-ball profiles, which are more general than the simple thin-wall limit. It is seen that the magnification characteristics may be very distinct, depending on the actual details of the solution, even for astrophysical Q-balls having the same size and mass. Assuming that such astrophysical Q-balls may form a small component of the dark matter in the Universe, we place limits on this fraction from the gravitational microlensing surveys EROS-2, OGLE-IV, HSC-Subaru and the proposed future survey WFIRST. Exploring various astrophysical Q-ball profiles and sizes, it is found that while for most intermediate masses that we consider, the dark matter fraction comprising astrophysical Q-balls is at most subpercent, for other masses it may be significantly higher. Published by the American Physical Society 2024

Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π2(S2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.

The New Soliton Configurations of the 3D Fractional Model in Arising Shallow Water Waves

The New Soliton Configurations of the 3D Fractional Model in Arising Shallow Water Waves

Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

AbstractA theory of nonassociative geometric flows is formulated as an extension of a string‐inspired model of nonassociative gravity determined by star product. The nonassociative Ricci tensor and curvature scalar defined by (non) symmetric metric structures and generalized (non) linear connections are used for defining nonassociative versions of Grigori Perelman F‐ and W‐functionals for Ricci flows and computing associated thermodynamic variables. The anholonomic frame and connection deformation method, AFCDM, which allows us to construct exact and parametric solutions describing nonassociative geometric flow evolution scenarios and modified Ricci soliton configurations with quasi‐stationary generic off‐diagonal metrics are developed and applied. There are provided explicit examples of solutions modeling geometric and statistical thermodynamic evolution on a temperature‐like parameter of modified black hole configurations encoding nonassociative star‐product and R‐flux deformation data. Further perspectives of the paper are motivated by nonassociative off‐diagonal geometric flow extensions of the swampland program, related conjectures and claims on geometric and physical properties of new classes of quasi‐stationary Ricci flow and black hole solutions.

Spherically Symmetric Non-Topological Solitons and Boson Stars in Friedberg-Lee-Sirlin Model

We study spherically symmetric non-topological solitons and boson stars in Friedberg-Lee-Sirlin model in 3+1 dimensional spacetime. The non-topological soliton field configuration consists of a massless complex scalar field coupled to a real scalar field with symmetry breaking potential. The complex scalar field becomes massive when the real scalar field goes to one of the degenerate vacuums. Their existence is supported by the conserved charge and the mass-energy only on certain frequency range. When gravity is taken into account, they form configuration called boson stars. The gravitational interaction influences the quantity of the conserved charge and the mass-energy of the system. We present the dependence of symmetry breaking energy scale on the solution of boson stars.

On nonlinear optical solitons of fractional Biswas-Arshed Model with beta derivative

The Biswas-Arshed (BA) model is an essential wave propagation model in nonlinear optics and optical fibers. In this manuscript, the enhanced G′/G-expansion method is taken into consideration. The BA model is used with this technique to locate visual soliton solutions. The solutions to the hyperbolic and trigonometric functions are determined using this technique. Each solution includes a large number of model and method parameters. The wave solutions are defined by the waves' character, which is determined by the three-dimensional (3D) and two-dimensional (2D) wave patterns with varying parameter values. The structure of the soliton shifts depending on the specific values of the parameters. These shifts are reflected in the 2D pictures that demonstrate the various soliton configurations. Finally, the obtained soliton solutions can be applied to high-speed data transmission to describe propagation pulses and to transmit light between two ends in optical fibers and communication systems.

Spinor walls in five-dimensional warped spacetime

We study domain wall solutions of a real spinor field coupling with gravitation in five dimensions. We find that the nonlinear spinor field supports a class of soliton configurations which could be viewed as a wall embedded in five dimensions. We begin with an illuminating solution of the spinor field in the absence of gravitation. In a further investigation, we exhibit three sets of solutions of the spinor field with nonconstant curvature bulk spacetimes and three sets of solutions corresponding to three constant curvature bulk spacetimes. We demonstrate that some of these solutions in specific conditions have the energy density distributions of domain walls for the spinor field, where the scalar curvature is regular everywhere. Therefore, the configurations of these walls can be interpreted as spinor walls which are interesting spinor field realizations of domain walls. In order to investigate the stability of these spinor configurations, the linear perturbations are considered. The localization of the zero mode of tensor perturbation is also discussed.

Electrically tunable collective motion of dissipative solitons in chiral nematic films

From the motion of fish and birds, to migrating herds of ungulates, collective motion has attracted people for centuries. Active soft matter exhibits a plethora of emergent dynamic behaviors that mimic those of biological systems. Here we introduce an active system composed of dynamic dissipative solitons, i.e. directrons, which mimics the collective motion of living systems. Although the directrons are inanimate, artificial particle-like solitonic field configurations, they locally align their motions like their biological counterparts. Driven by external electric fields, hundreds of directrons are generated in a chiral nematic film. They start with random motions but self-organize into flocks and synchronize their motions. The directron flocks exhibit rich dynamic behaviors and induce population density fluctuations far larger than those in thermal equilibrium systems. They exhibit “turbulent” swimming patterns manifested by transient vortices and jets. They even distinguish topological defects, heading towards defects of positive topological strength and avoiding negative ones.

Steeping and dispersive effects analysis of a couple of long-wave equations in dispersive media

Dispersive wave propagations are described by nonlinear models, such as regularized long waves and modified regularized long waves, where nonlinearity and dispersion are important aspects of wave evolution to model long-wave propagation in dispersive media with small amplitudes. In this article, solitary wave solutions to the formerly indicated nonlinear equations are computed as exponential, hyperbolic, and trigonometric structures and their integration by balancing the steeping and dispersion terms of the highest order, and different classes of definitive localized coherent structures with their interaction properties, such as soliton solutions, are extracted by assigning appropriate functions. We have also investigated the impact of steeping and wave spread on waveforms. The wave solutions are assessed using the enhanced modified simple equation approach, which organizes the soliton solutions based on the features of the dispersive interconnections with the nonlinear cubic and quadratic characters that exist in the equations. The consistent 3D and 2D soliton configurations show that the wave profile is modulated by the wave velocity function and the parameters associated with it, and most of the modulation is due to linear effects.

Enormous soliton solutions to a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

In our current study, we will extract enormous, impressive soliton solutions to a (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semi classical limit. The suggested model has its wide importance for many magnetism phenomena. Specially, it is very momentous in modern magnetism theory in which the nonlinear long-range ferromagnetic ordering magnetism can be explained. Moreover, it describes the characteristic of magnetism to many insulating crystals as well as interaction spins. The ferromagnetism plays fundamental role in modern technology and industry and it is principal for many electrical and electromechanical devices such as electromagnets, electric motors, generators etc. We will document various types of the soliton solutions by using four various techniques to extract the soliton configuration behaviors arising from the magnet dynamics model. The techniques that are used to derive these types of soliton solutions are the extended direct algebraic method, the extended simple equation method, the solitary wave ansatz method and the Paul-Painleve approach method. The expected achieved soliton solutions will offer a rich podium to study the nonlinear spin dynamics in magnetic materials. The achieved soliton solutions are new compared with that achieved previously by other authors who used different techniques.

Low-energy effective quantum field theoretic description of excitations about soliton configurations

Solitons are the classical field configurations connecting two trivial vacua. These are also the solutions of classical field equations of motion with particle-like properties. Moreover, they are localized in space, having finite energy, and are stable against decay into radiation. The coherent state description of kink-solitons is discussed in the present article. Further, the relation between topological solitons and occupation numbers corresponding to low momentum excitations are also discussed coherently. The description of the low energy excitations about solitons in quantum field theory is the main theme of this article. Further, a few physical observables, namely some low order correlation functions, are computed up to certain integral forms. Furthermore, we have shown that it is possible to detect the presence of soliton-like classical configurations in many-particle systems from the nature of the one-point function and non-conservation of momentum feature of one-point, two-point and three-point functions in this low-energy effective field theory of these excitations.

Solitons in curved spacetime

Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling transformation. According to this theorem, the dimension is the critical dimension for the existence of solitons in scalar field theories without the gauge fields. In the present article, Derrick's theorem is extended in a generic curved spacetime in a covariant manner. Moreover, the existence of solitons in conformally flat spacetimes and spherically symmetric spacetimes is also shown using the approach presented in this article. Further, the approach shown in the present article in order to derive the soliton configurations is not restricted to a particular form of the field potential or curved spacetime.

Positive energy warp drive from hidden geometric structures

Warp drives in Einstein’s general theory of relativity provide a unique mechanism for manned interstellar travel. It is well-known that the classical superluminal soliton spacetimes require negative energy densities, likely sourced by quantum processes of the uncertainty principle. It has even been claimed by few that negative energy densities are a requirement of superluminal motion. However, recent studies suggest this may not be the case. A general decomposition of the defining variables and the corresponding decomposition of the Eulerian energy are studied. A geometrical interpretation of the Eulerian energy is found, shedding new light on superluminal solitons generated by realistic energy distributions. With this new interpretation, it becomes a relatively simple matter to generate solitonic configurations, within a certain subclass, that respect the positive energy constraint. Using this newfound interpretation, a superluminal solitonic spacetime is presented that possesses positive semi-definite energy. A modest numerical analysis is carried out on a set of example configurations, finding total energy requirements four orders of magnitude smaller than the solar mass. Extraordinarily, the example configurations are generated by purely positive energy densities, a tremendous improvement on the classical configurations. The geometrical interpretation of the Eulerian energy thus opens new doors to generating realistic warp fields for laboratory study and potential future manned interstellar travel.

De Sitter vacua in the string landscape

The late-time behavior of our universe is one of accelerated expansion, or that of a de Sitter space, and therefore motivates us to look for time-dependent backgrounds. Finding such backgrounds in string theory has always been a challenging problem. An even harder problem is to find time-dependent backgrounds that allow positive dark energies. As a first step to handle such scenarios, we study a time-dependent background in type IIB theory, with four-dimensional de Sitter isometries, by uplifting it to M-theory and then realizing it as a coherent, or squeezed-coherent, state over an appropriate solitonic configuration. While classically such a background does not solve the equations of motion, the corresponding Schwinger-Dyson equations reveal that there are deeper issues that may even prohibit a solution to exist at the quantum level, as long as the internal space remains time-independent. A more generic analysis is then called for, where both the effective four-dimensional space-time, the internal space, and the background fluxes are all time-dependent. We study in details such a background by including perturbative and non-perturbative as well as local and non-local quantum terms. Our analysis reveals a distinct possibility of the emergence of a four-dimensional positive curvature space-time with de Sitter isometries and time-independent Newton's constant in the landscape of type IIB string theory. We argue how the no-go and the swampland criteria are avoided in generating such a background, and compare it with other possibilities involving backgrounds with time-dependent Newton constants. These time-varying Newton constant backgrounds typically lead to unavoidable late time singularities, amongst other issues.

New soliton configurations for two different models related to the nonlinear Schrödinger equation through a graded-index waveguide

The present paper studies two various models with two different types: the nonlinear Schrödinger equation with power-law nonlinearity and the (3 + 1)-dimensional nonlinear Schrödinger equation. We perform the modified (G′G)-expansion method to find some exact solutions and to construct various types of solitary wave phenomena for each equation. The received aspects contribute to the firm mathematical foundation and might be essential to the soliton waves. As a result, we obtain all the solutions from Wazwaz [Math. Comput. Modell. 43, 178–184 (2016)] and also obtain some new soliton solutions.

Complex systems of Kuramoto–sine-Gordon solitons

The 1 + 1 dimensional Kuramoto–sine-Gordon system consists of a set of N nonlinear coupled equations for N scalar fields θ i , which constitute the nodes of a complex system. These scalar fields interact by means of Kuramoto nonlinearities over a network of connections determined by N(N − 1)/2 symmetric coupling coefficients a ij . This system, regarded as a chirally invariant quantum field theory, describes a single decoupled massless field together with N − 1 scalar boson excitations of nonzero mass depending on a ij , which propagate and interact over the network. For N = 2 the equations decouple into separate sine-Gordon and wave equations. The system allows an extensive array of soliton configurations which interpolate between the various minima of the 2π-periodic potential, including sine-Gordon solitons in both static and time-dependent form, as well as double sine-Gordon solitons which can be imbedded into the system for any N. The precise form of the stable soliton depends critically on the coupling coefficients a ij . We investigate specific configurations for N = 3 by classifying all possible potentials, and use the symmetries of the system to construct static solitons in both exact and numerical form.

Solitons in a class of interacting scalar field theories without SO(2) invariance

In this ppaer, we study kink soliton configurations in interacting scalar field theories containing two fields without [Formula: see text] invariance. We study a class of such theories, the well-known Montonen–Sarker–Trullinger–Bishop model is one of them. These models are interesting since the [Formula: see text] current is not conserved in them due to the presence of explicit symmetry breaking terms in the action. The existence of kink soliton configurations is shown in terms of a system of first-order ordinary differential equations. Although [Formula: see text] current in these models is nonconserved, our approach is general enough to study soliton configurations in a generic two interacting scalar field theory. We also discuss other benefits of this approach.