Soliton Phase Research Articles

Observation of Two-Dimensional Dam Break Flow and a Gaseous Phase of Solitons in a Photon Fluid.

We report the observation of a two-dimensional (2D) dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to 2D nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D soliton gas in integrable systems. We measure the statistical features of this gaslike phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.

Optical solitons for the concatenation model with differential group delay having multiplicative white noise by F–expansion approach

This study examines optical soliton solutions for the concatenation model, which includes differential group delay and white noise in both components. Through the F–expansion integration algorithm, an extensive spectrum of soliton solutions was found. It has been confirmed that white noise affects the phase of solitons along both components.

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.

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

Dynamics of the Davydov’s soliton in external oscillating magnetic field

The influence of an external oscillating in time magnetic field on the dynamics of the Davydov’s soliton is studied. It is shown that soliton parameters depend on the amplitude and frequency of the magnetic field, as well as on the field orientation with respect to the molecular chain axis. Electron dynamics in the parallel magnetic field is a composition of the “free” soliton coherent propagation along the molecular chain and oscillatory movement in the transverse direction. The latter is described by the functions of the harmonic oscillator with the cyclotron frequency depending on the field frequency. In a perpendicular field the soliton dynamics is a superposition of (i) the free electron plane wave in the plane perpendicular to the molecular chain, and (ii) propagation along the chain which is described by the modified Nonlinear Schrödinger equation with an extra term depending on the field. This equation is solved using the nonlinear perturbation theory. It is shown that the soliton velocity and phase are given by expressions which include the terms oscillating in time with the frequency of the main harmonic, given by the external field frequency, and higher multiple harmonics. Such complex effects of external time-depending magnetic fields on the dynamics of solitons modify the charge transport in low-dimensional molecular systems, which in its turn, can affect the functioning of the devices based on such compounds. These results suggest also the physical mechanism of therapeutic effects of oscillating magnetic fields, based on the field influence on the dynamics of solitons which provide charge transport through biological macromolecules in the redox processes.

Pattern transformation and control of generalized multi-peak breathing solitons induced by transverse cross modulation

Based on the nonlocal nonlinear Schrödinger equation, the pattern transformation and control of transverse cross-modulated sine-Gaussian (TCMSG) breathing solitons during transmission are studied. Several expressions have been derived, including the transmission, soliton width, phase wavefront curvature, and so on. The study demonstrates that the coefficient of transverse cross modulation term controls the pattern transformation of the TCMSG breathing solitons. TCMSG breathing solitons can form generalized spatial solitons and breathers during transmission. The variation of the soliton width extrema and their change rates with the transverse cross modulation term coefficient is investigated. The influence of the initial incident power and the transverse cross modulation term coefficient on the soliton width change rate and phase wavefront curvature extrema is studied.

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.

Generalized cosine-Gaussian breathing solitons with transverse cross modulation in nonlocal nonlinear media

Based on the nonlocal nonlinear Schrödinger equation, the propagation characteristics of transverse cross-modulated cosine-Gaussian (TCMCG) breathing solitons in strongly nonlocal media are studied. A series of mathematical expressions are provided to describe the propagation dynamics characteristics of the TCMCG breathing solitons, including the soliton width, soliton width change rate, soliton width extreme values, change rates of soliton width extreme values, phase wavefront curvature and phase wavefront curvature extreme values, etc. The research results indicate that by modulating TCMCG breathing solitons, generalized high-order spatial solitons can be formed with periodic changes in light intensity modes but unchanged in beam width. The cosine function parameter has a significant impact on the propagation dynamics characteristics, which appears in the initial expression and plays a cross modulation role in the transverse spatial light intensity. The effect of the initial incident power on soliton width extreme values and phase wavefront curvature extreme values is also discussed.

One-dimensional topological phase and tunable soliton states in atomic nanolines on Si(001) surface

Formation of exotic topological states on technologically important semiconductor substrate is significant from the aspects of both fundamental research and practical implementation. Here, we demonstrate one-dimensional (1D) topological phase and tunable soliton states in atomic nanolines self-assembled on Si(001) surface. By first-principles calculations and tight-binding modeling, we reveal that Bi nanolines provide an ideal system to realize a multi-orbital Su–Schrieffer–Heeger (SSH) model, and the electronic properties can be modulated by substrate-orbital-filtering effect. The topological features are confirmed by nontrivial end states for a finite-length nanoline and (anti-)soliton states at the boundary of two topologically distinct phases. We demonstrate that solitons are highly mobile on the surface, and their formation could be controlled by surface B/N doping. As these nanolines can extend several micrometers long without kinks, and quantum transport simulations suggest clear signatures of topological states characterized by transmission resonance peaks, our work paves an avenue to achieve 1D topological phase compatible with semiconductor technology and to engineer the properties with high tunability and fidelity for quantum information processing.

Effect of nonthermal and nonextensive electrons on dust acoustic waves in planetary rings

AbstractDust acoustic waves (DAWs) in plasmas are influenced by many plasma parameters, such as, ion temperature, electron number density, nonthermal and nonextensive parameters, and dust cyclotron frequency. The plasma system is described by plasma fluid equations. The Zakharov–Kuznetsov equation and instability growth rate of DAWs have been obtained by reductive perturbation method and small‐ expansion method, respectively. The effects of plasma parameters on the linear dispersion relation, phase velocity, amplitude, width, soliton energy, and three‐dimensional instability of DAWs have been carried out. It is obvious that the incremental nonextensive (nonthermal) parameter leads to the shrinking (incremental) soliton energy and phase velocity. These results are useful for understanding dusty plasma dynamics with Cairns–Tsallis electrons in planetary rings.

Unveiling solitons and dynamic patterns for a (3+1)-dimensional model describing nonlinear wave motion

<abstract><p>In this study, the underlying traits of the new wave equation in extended (3+1) dimensions, utilized in the field of plasma physics and fluids to comprehend nonlinear wave scenarios in various physical systems, were explored. Furthermore, this investigation enhanced comprehension of the characteristics of nonlinear waves present in seas and oceans. The analytical solutions of models under consideration were retrieved using the sub-equation approach and Sardar sub-equation approach. A diverse range of solitons, including bright, dark, combined dark-bright, and periodic singular solitons, was made available through the proposed methods. These solutions were illustrated through visual depictions utilizing 2D, 3D, and density plots with carefully chosen parameters. Subsequently, an analysis of the dynamical nature of the model was undertaken, encompassing various aspects such as bifurcation, chaos, and sensitivity. Bifurcation analysis was conducted via phase portraits at critical points, revealing the system's transition dynamics. Introducing an external periodic force induced chaotic phenomena in the dynamical system, which were visualized through time plots, two-dimensional plots, three-dimensional plots, and the presentation of Lyapunov exponents. Furthermore, the sensitivity analysis of the investigated model was executed utilizing the Runge-Kutta method. The obtained findings indicated the efficacy of the presented approaches for analyzing phase portraits and solitons over a wider range of nonlinear systems.</p></abstract>

A novel investigation of dynamical behavior to describe nonlinear wave motion in (3+1)-dimensions

This study focuses on the extended (3+1)-dimensional Sakovich equation, which is utilized for the description of nonlinear wave motion and manifests increased dispersion and nonlinear effects within the realm of nonlinear dynamics. The Lie symmetries are initially identified, followed by the construction of the Abelian algebra corresponding to these symmetries. Through the utilization of this Abelian algebra, the governing equation is transformed into an ordinary differential equation. Precise solutions are obtained using the unified technique, and the results are visually represented through 3D, 2D, and contour plots. Subsequently, the qualitative behavior of the equation is explored from multiple perspectives, encompassing bifurcation, chaos, and sensitivity analysis. Bifurcation is examined at critical points, while the dynamical system is subjected to an external force, leading to the detection of chaotic behavior employing diverse tools such as 3D and 2D phase portraits, time series, Poincaré maps, and multistability analysis. Furthermore, sensitivity analysis is conducted for various initial values, revealing the considerable sensitivity of the presented model, wherein even slight changes in the initial conditions result in significant variations. The reported outcomes are intriguing, showcasing the efficacy and applicability of the suggested methodologies for the assessment of soliton solutions and phase patterns in a diverse range of nonlinear models.

Multiple-q current states in a multicomponent superconducting channel

It is well-established that multicomponent superconductors can host different nonstandard phenomena such as broken-time reversal symmetry (BTRS) states, exotic Fulde–Ferrell–Larkin–Ovchinnikov phases, the fractional Josephson effect as well as plenty of topological defects like phase solitons, domain walls and unusual vortex structures. We show that in the case of a two-component superconducting quasi-one-dimensional channel this catalogue can be extended by a novel inhomogeneous current state, which we have termed as a multiple-q state, characterized by the coexistence of two different interpenetrating Cooper pair condensates with different total momenta. Within the Ginzburg–Landau formalism for a dirty two-band superconductor with sizable impurity scattering treated in the Born-approximation we reveal that under certain conditions, the occurrence of multiple-q states can induce a cascade of transitions involving switching between them and the homogeneous BTRS (non-BTRS) states and vice versa leading this way to a complex interplay of homogeneous and inhomogeneous current states. We find that hallmarks of such a multiple-q state within a thin wire or channel can be a saw-like dependence of the depairing current and the existence of two distinct stable branches on it (a bistable current state).

Further physical research about soliton structures and phase portraits in nonlinear fractional electrical transmission line model

This paper presents several novel contributions in the field of nonlinear fractional low-pass electrical transmission line model (NFLETLM). Firstly, using the modified (G′G2)-expansion method and the extended modified Jacobi elliptic expansion method, we discovered new and accurate solutions for NFLETLM, which have not been reported in the existing literature (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). These solutions, denoted as U3,U4,U7,U8,U9,U10,U13,U14 and UJ1,UJ2,UJ3,UJ4 represent novel contributions to the fields. Secondly, by utilizing computer simulations, we observed various intriguing phenomena in the wave solution graphs, such as anti-kink waves, periodic waves, intense singular periodic waves, bright singular wave solutions, multi-periodic waves, intense double periodic waves, and alternating patterns of light and shade waves. These findings shed light on previously unexplored aspects of the problem. Thirdly, through an extensive study on the newly discovered solutions, we provided a comprehensive understanding of the solitons inherent in the NFLETLM, including comparison with other derivative solutions. Our conformable fractional derivative solutions showed similarities to beta derivative solutions, distinguishing them from Riemann–Liouville derivative solutions. Lastly, we explored the phase portrait, bifurcation analysis, sensitivity, and potential chaotic behaviors of the NFLETLM, which have not been addressed in previous works (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). This innovative contribution expands our understanding of the NFLETLM model and uncovers new dynamics and phenomena.

On the distinction of seasonal internal solitary waves characteristics in the Lombok Strait based on multi-satellite data

ABSTRACT This study presents a multi-satellite approach utilizing synthetic aperture radar (SAR) and optical sensors to distinguish the characteristics of internal solitary waves (ISWs) during different seasons in the Lombok Strait. SAR and optical sensors are employed to estimate the dynamic parameters (soliton number, wavelength, and phase speed) of ISWs during different seasons based on the detected ISW patterns. ISW characteristics in the Lombok Strait during two seasons were observed using Sentinel-1/SAR, GCOM-C/SGLI, and Terra/MODIS sensors. Results indicated that Sentinel-1/SAR detected a higher soliton number for the northward-propagating ISWs in the Lombok Strait during the north-west monsoon (NWM) than the south-east monsoon (SEM) period. The identified wavelengths of ISWs were wider during the SEM than during the NWM whenever two packets were detected in one image. Similar variations were observed by optical sensors (SGLI and MODIS). Estimation of ISW phase speed derived from multi-satellite images and the Korteweg-de Vries (KdV) equation showed that the phase speed was faster during the NWM than the SEM. These results correlated with the seasonal variation of thermocline depth and density differences between the two layers. Because of the bias caused by turbid water, a pattern of high chlorophyll-a was observed during the NWM period in the SGLI, MODIS, and VIIRS products. Propagation of turbid water to the north was assumed to be a result of the intense ISW activity in this area. Highly variable currents due to ISW activity in the Lombok Strait area were assumed to cause the anomalous sediment transport in this study. The multi-satellite observation data used in this study enhanced understanding of the influence of ISWs on coastal interactions in the Lombok Strait.

Helitronics as a potential building block for classical and unconventional computing

Magnetic textures are promising candidates for unconventional computing due to their non-linear dynamics. We propose to investigate the rich variety of seemingly trivial lamellar magnetic phases, e.g. helical, spiral, stripy phase, or other one-dimensional soliton lattices. These are the natural stray field-free ground states of almost every magnet. The order parameters of these phases may be of potential interest for both classical and unconventional computing, which we refer to as helitronics. For the particular case of a chiral magnet and its helical phase, we use micromagnetic simulations to demonstrate the working principles of all-electrical (i) classical binary memory cells and (ii) memristors and artificial synapses, based on the orientation of the helical stripes.

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

AbstractThe mathematical description of localized solitons in the presence of large‐scale waves is a fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear optics, and condensed matter physics. Here, the evolution of a soliton as it interacts with a rarefaction wave or a dispersive shock wave, examples of slowly varying and rapidly oscillating dispersive mean fields, for the Korteweg–de Vries equation is studied. Step boundary conditions give rise to either a rarefaction wave (step up) or a dispersive shock wave (step down). When a soliton interacts with one of these mean fields, it can either transmit through (tunnel) or become embedded (trapped) inside, depending on its initial amplitude and position. A topical review of three separate analytical approaches is undertaken to describe these interactions. First, a basic soliton perturbation theory is introduced that is found to capture the solution dynamics for soliton–rarefaction wave interaction in the small dispersion limit. Next, multiphase Whitham modulation theory and its finite‐gap description are used to describe soliton–rarefaction wave and soliton–dispersive shock wave interactions. Lastly, a spectral description and an exact solution of the initial value problem is obtained through the inverse scattering transform. For transmitted solitons, far‐field asymptotics reveal the soliton phase shift through either type of wave mentioned above. In the trapped case, there is no proper eigenvalue in the spectral description, implying that the evolution does not involve a proper soliton solution. These approaches are consistent, agree with direct numerical simulation, and accurately describe different aspects of solitary wave–mean field interaction.

The Analysis of Bifurcation, Quasi-Periodic and Solitons Patterns to the New Form of the Generalized q-Deformed Sinh-Gordon Equation

In this manuscript, a new form of the generalized q-deformed Sinh-Gordon equation is investigated which could model physical systems with broken symmetries and to incorporate phenomena involving amplification or dissipation. The proposed model is explored based on the Lie symmetry approach. Using similarity reduction, the partial differential equation is transformed into an ordinary differential equation. By employing the generalized auxiliary equation approach, precise results for the derived equation are obtained. The solutions are graphically depicted as 3D, 2D, and contour plots. Furthermore, the qualitative analysis of the considered model is investigated by employing the concepts of bifurcation and chaos. The phase profiles are displayed for different sets of the parameters. Additionally, by applying an external periodic strength, quasi-periodic and chaotic behaviors are documented. Various tools for detecting chaos are discussed, including 3D and 2D phase patterns, time series, and Poincaré maps. Additionally, a sensitivity analysis is conducted for various initial conditions. The obtained findings are unique and indicate the viability and efficacy of the suggested strategies for evaluating soliton solutions and phase illustrations for various nonlinear models.

Crossover of critical behavior and nontrivial magnetism in the chiral soliton lattice host Cr1/3TaS2

The chiral magnetic soliton, a topological kinklike spin texture, has significant applications in spintronic components. In this work, a crossover of critical behavior is found in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$, a chiral magnetic soliton host with the highest ${T}_{C}$ to date. Angular-dependent magnetization reveals that ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$ exhibits an easy orientation within the isotropic $ab$ plane, but displays anisotropy with the $c$ axis. By using a modified iterative method, two distinct sets of critical exponents, including ${\ensuremath{\beta}}_{\ensuremath{-}}=0.3190(1)$ and ${\ensuremath{\gamma}}_{\ensuremath{-}}=1.263(8)$ for $T\ensuremath{\le}{T}_{C}$, and ${\ensuremath{\beta}}_{+}=0.3475(2)$ and ${\ensuremath{\gamma}}_{+}=1.385(5)$ for $T\ensuremath{\ge}{T}_{C}$, are acquired on both sides of the transition. Analysis of the exponents indicates a crossover of the magnetic interaction from a three-dimensional Ising type below ${T}_{C}$ to a three-dimensional Heisenberg type above ${T}_{C}$, implying nontrivial magnetism in this system. Based on universality scaling, a detailed $H\ensuremath{-}T$ phase diagram around ${T}_{C}$ is constructed for $H\ensuremath{\perp}c$. The crossover of the critical behavior in ${\mathrm{Cr}}_{1/3}{\mathrm{TaS}}_{2}$ is peculiar to chiral magnetic soliton hosts, suggesting that the three-dimensional magnetic coupling is replaced by a one-dimensional one in the chiral magnetic soliton phase via a phase transition.

Islands of chiral solitons in integer-spin Kitaev chains

An intriguing chiral soliton phase has recently been identified in the $S=\frac{1}{2}$ Kitaev spin chain. Here we show that for $S$ = 1, 2, 3, 4, 5 an analogous phase can be identified, but contrary to the $S=\frac{1}{2}$ case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adiabatically connect the integer spin Kitaev chain to the polarized phase. Only at sizable intermediate fields along symmetry directions does the soliton phase appear centered around the special point ${h}_{x}^{★}={h}_{y}^{★}=S$ where two exact product ground states can be identified. The large-$S$ limit can be understood from a semiclassical analysis, and variational calculations provide a detailed picture of the $S=1$ soliton phase. Under open boundary conditions, the chain has a single soliton in the ground state, which can be excited, leading to a proliferation of in-gap states. In contrast, even length periodic chains exhibit a gap above a twice-degenerate ground state. The presence of solitons leaves a distinct imprint on the low-temperature specific heat.