Soliton Structures Research Articles

Superthermal electron’s effects on lump solitons structures in magnetized auroral plasma

Based on the considerations of the acknowledgements of the numerous space observations by satellites in the auroral plasma, astrophysics plasmas, spacecraft observations, various plasma models have been framed and revealed different interesting features, like electrostatic structures, solitary waves, double layers, supersolitons, etc. Soliton theory is a very efficient and competent way to describe nonlinear features. Using Viking satellite data in the auroral plasma, we have derived lump soliton solutions of the Kadomstev-Petviashvili (KP) equation by employing Hirota bilinear method. Due to its wide range of applications, the study of lump soliton is very attractive and important too. It has been shown that the lump solitons structures as well as in the one-dimensional form of lump soliton are varied with associated parameters in the auroral magnetized plasma. During the analysis of the features of the lump solitons, it is found that the system parameters play a pivotal role on the lump solitons structures.

Linear and nonlinear analysis of Ion-Temperature-Gradient (ITG) driven mode in the asymmetric pair-ion magnetoplasma

We have investigated linear and nonlinear dynamics of ion-temperature-gradient (ITG) driven drift mode for Maxwellian and non Maxwellian pair-ion plasma embedded in an inhomogeneous magnetic field having gradients in the temperature and number density of ions. Linear dispersion relations are derived and analyzed analytically as well as numerically for different cases. It has been found that growth rate of instability increases with increasing η. By using the transport equations of Braginskii, model, a set of nonlinear equations are derived. In the nonlinear regime, soliton structures are found to exist. Our numerical analysis shows that amplitude of solitary waves increases by increasing ion to electron number density ratio. These solitary structures are also found to be sensitive to asymmetries in pair plasma and non thermal kappa and Cairns distributed electrons. Our present work may contribute a good illustration of the observation of nonlinear solitary waves driven by the ITG mode in magnetically confined pair-ion plasmas and space pair-ion plasmas as the formation of localized structures along drift modes is one of the striking reasons for L-H transition in the region of improved confinements in magnetically confined devices like tokamaks.

1D solitons in cubic-quintic fractional nonlinear Schrödinger model

We examine the properties of a soliton solution of the fractional Schrö dinger equation with cubic-quintic nonlinearity. Using analytical (variational) and numerical arguments, we have shown that the substitution of the ordinary Laplacian in the Schrödinger equation by its fractional counterpart with Lévy index alpha permits to stabilize the soliton texture in the wide range of its parameters (nonlinearity coefficients and alpha) values. Our studies of omega (N) dependence (omega is soliton frequency and N its norm) permit to acquire the regions of existence and stability of the fractional soliton solution. For that we use famous Vakhitov-Kolokolov (VK) criterion. The variational results are confirmed by numerical solution of a one-dimensional cubic-quintic nonlinear Schrödinger equation. Direct numerical simulations of the linear stability problem of soliton texture gives the same soliton stability boundary as within variational method. Thus we confirm that simple variational approach combined with VK criterion gives reliable information about soliton structure and stability in our model. Our results may be relevant to both optical solitons and Bose-Einstein condensates in cold atomic gases.

Nonplanar ion-acoustic solitons and shocks with superthermal trapped electrons and transverse perturbations

The formation and propagation of nonlinear ion-acoustic (IA) waves are studied in an unmagnetized cold viscous plasma, comprising the inertial ions and superthermal trapped electrons in cylindrical geometry with transverse perturbations. The well-known reductive perturbation method is employed to derive cylindrical trapped Kadomtsev Petviashvili Burgers (CTKPB) and cylindrical trapped Kadomtsev Petviashvili (CTKP) equations with and without dissipation effects, respectively. The exact solutions of CTKPB and CTKP equations are obtained for the first time by utilizing the dependent variable transformation. The soliton and shock structures are found to be significantly affected by the plasma parameters including the trapping efficiency parameter β, the superthermality parameter κ, viscosity µ 0 and the geometrical effects. Importantly, the geometrical effects and transverse perturbations alter the shape of solitons and shocks, resulting into the parabolic nonlinear structures. These structures become more parabolic at later times due to an interplay of transverse and time coordinates (η, τ). The results of the present study might be helpful to understand the characteristics of IA structures in space plasmas, such as auroral regions, where energetic trapped electrons have been observed.

Observation of kinked soliton structure in realistic materials through wave packet simulations

In this work, we report the observation of a kinked structure in single-layer graphene through phonon wave packet simulations. The observed kinked structure agrees very well with the tanh-form solution of the soliton wave, and its group velocity increases with increasing kink amplitude, which suggests that the kinked structure has a soliton nature. This conclusion is further supported by the separate soliton wave packet simulations, in which consistent results with the phonon wave packet simulations are obtained. Our study provides a useful platform to study the soliton wave transport in realistic materials.

The envelope soliton for the nonlinear interaction of Langmuir waves with electron acoustic waves in the Earth's inner magnetosphere

The nonlinear coupling of Langmuir waves with electron-acoustic waves is investigated using the kinetic theory, where the hot electron component is modeled by the kappa distribution with an exponential cutoff at high energy tail, i.e., the cutoff kappa distribution. The one dimensional structure of envelope Langmuir solitons is analyzed by the numerical calculation with parameters typical of the Earth's inner magnetosphere. In the case of hot electrons with a cutoff kappa distribution, envelope Langmuir solitons have larger width and slower speed than that in the case of hot electrons with a Maxwellian distribution. The envelop Langmuir soliton with density depletion obtained in the Earth's inner magnetosphere propagates at a speed lower than the electron-acoustic velocity. At a given amplitude of electrostatic field, the envelope Langmuir soltions have a speed comparable with the ones of electron-acoustic wave solitons, but a wider scale in the case of hot electrons with a cutoff kappa distribution.

Chirped self-similar localized pulses on a continuous wave background in presence of cubic–quintic nonlinearity and self-frequency shift

We investigate the nonlinear pulse propagation through an inhomogeneous single-mode optical fiber where the evolution dynamics is governed by the generalized higher-order nonlinear Schrödinger equation with varying group velocity dispersion, cubic and quintic nonlinearities, self-frequency shift arising from stimulated Raman scattering, and linear gain or loss. A new class of soliton pulse solutions for a wave field is constructed based on the similarity transformation connecting with the constant-coefficient Kundu–Eckhaus equation. This class describes soliton structures that propagate self-similarity on a continuous-wave (cw) background, and acquires a nonlinear chirp as it propagates in the inhomogeneous fiber medium. It is found that the nonlinear chirp associated with these self-similar pulses originates essentially from the self-frequency shift effect. The conditions on fiber parameters for the existence of those nonlinearly chirped self-similar localized pulses are also given. As a practical example, we studied their evolution dynamics in a specified soliton control system. The solution stability against perturbation is checked by direct numerical simulation.

A variety of new soliton structures and various dynamical behaviors of a discrete electrical lattice with nonlinear dispersion via variety of analytical architectures

Nonlinear electrical lattices are powerful experimental tool for studying nonlinear dispersive media and creating opportunities for the realistic modeling of electrical solitons. In this work, we adopt the generalized auxiliary equation methods, the first integral method, and the Möbius transformation approach to extract a variety of traveling and solitary wave solutions of the nonlinear Salerno equation describing the nonlinear discrete electrical lattice with nonlinear dispersion. The kink, antikink, dark, bright, peakons, antipeakons, and periodic wave solutions are all derived. The existence criteria of solitons are described. It has been shown that for the selective values of arbitrary constants in an auxiliary equation, the generalized auxiliary equation method II is reduced to the new ‐model expansion method as well as the new extended auxiliary equation method. The impact of free parameters on the obtained solutions is investigated and graphically depicted using physical descriptions. The acquired results are important for the validity of numerical and experimental results and further understanding of the wave propagation in the nonlinear discrete electrical lattice. In addition, the stability analysis of the obtained solitary wave solutions is studied. Furthermore, using the maple software, all derived solutions were checked by re‐entering them into the considered equation.

Diversity of optical soliton structures in the spinor Bose–Einstein condensate modeled by three-component Gross–Pitaevskii system

This paper pays attention to secure the different forms of optical soliton solutions to the spinor Bose–Einstein condensate. Three-component Gross–Pitaevskii (tc-GP) system which describes the F = 1 spinor Bose–Einstein condensate (BEC), with F denoting the atom’s spin, is used as a governing model to secure the solutions in BEC. Superfluidity and superconductivity are two properties of the low-temperature phenomenon that are associated with the BEC, which is formed by a diluted atomic gas. There has been an increasing interest in studying multi-component equations because they can be utilized to explain a wide range of complicated physical phenomena and have more dynamical structures of localized wave solutions. New extended direct algebraic method (NEDAM), a recently developed integration tool, is used to secure the solution. Different kinds of solitons, such as dark, singular, kink, bright–dark, complex and combined, are extracted. In addition, hyperbolic, exponential type and periodic solutions are guaranteed. Nonlinear partial differential equations (NLPDEs) are well-explained by the technique since it offers previously derived solutions and also extracts new exact solutions by incorporating the results of multiple procedures. In addition to discussing the physical representation of some solutions, we also plot 3D, 2D and contour graphs using the appropriate parameter values. The findings of this paper can improve the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the methodology used. We believe that a large number of engineering model specialists will benefit from this research. Findings suggest that the algorithm employed is efficient, prompt, succinct and applicable to complex systems.

Study of lump soliton structures in quantum electron‐positron‐ion magnetoplasma

AbstractSoliton theory is a very efficient and competent way to describe nonlinear features. Using Hirota bilinear method, we have obtained a lump soliton solution of the Kadomstev‐Petviashvili equation which is the reduced canonical form of the collisionless quantum electron‐positron‐ion magnetoplasma system. Due to its wide range of applications, the study of lump soliton structures is very much attractive and important. The amplitude of lump solitons is varied for different system parameters. During the analysis of the features of the lump solitons, it is found that the quantum diffraction parameter (He), statistical temperature ratio (σ), positrons number density (μp), magnetic intensity parameter (Ω) have a considerable impact on the lump solitons structures. Compressive as well as rarefactive lump soliton has been found during the investigation.

Impact of spectral filtering on the stability of a stationary dissipative soliton in the complex cubic–quintic Ginzburg–Landau equation in the presence of higher-order effects

In this work, we investigate the influence of linear and nonlinear effects on the stability of stationary solitons in the framework of the Complex Cubic–Quintic Ginzburg–Landau Equation (CCQGLE). In this regard, analytical and numerical results of the stationary soliton revealed the existence of two types of pulses in the stationary state for the given parameters. These pulses in the parameter space propagate with different amplitudes and frequencies. When the amplitude of a pulse increases (resp. decreases), its frequency decreases (resp. increases). In the first pulse (first fixed point), we obtained several dynamics (source, circle and sink) and we showed that there is a boundary between the source and sink dynamics. This boundary is the dynamics of an unstable limit cycle (subcritical bifurcation) representing the bifurcation in the sense of Poincaré–Andronov–Hopf (P. A. H). The second pulse (second fixed point), showed us a single dynamic called saddle. When we take a coordinate in the parameter space corresponding to a dynamics, we find that the structure of the soliton is preserved in the case of a sink, and is destroyed at a certain distance in the other cases. This proves that the soliton envelope is stable in the sink dynamics and unstable in the other dynamics (source, saddle and circle). We also plotted the bifurcation parameters as a function of the gain dispersion. This allowed us to highlight the areas corresponding to each dynamic. Direct numerical simulations of the perturbed CCQGLE confirmed our theoretical predictions. We observed the robustness of the stable soliton by superimposing the noise on the initial pulse and found that the soliton structure is preserved up to a certain limit. These results can allow us to transmit information over long distances.

Q-Deformed solitary pulses in the higher-order nonlinear Schrödinger equation with cubic-quintic nonlinear terms

We investigate the existence and propagation properties of deformed solitary pulses in a non-Kerr medium described by the higher-order nonlinear Schrödinger equation with cubic-quintic nonlinear terms and third-order dispersion. Two different types of exact analytical q-deformed soliton solutions have been derived by means of the ansatz method. The results show that both width and amplitude of the soliton structures are influenced by the deformed factor. It is found that the introduced deformed factor lets the soliton solution deviates from the standard profile. The requirements on the parameters of the non-Kerr material for the existence of these localized structures are presented. By employing numerical simulations, we demonstrate the stability of these deformed soliton solutions under the finite perturbations. Finally, the collision between similar soliton pulses is also investigated.

Observation of complex multimode soliton molecules in spatiotemporal mode-locked Er-doped fiber laser

In this letter, we have reported experimental observation of diverse structural multimode (MM) soliton molecules in an all fiber spatiotemporal mode-locked (STML) laser. By adjusting the intracavity devices, the STML operation state at ∼1560 nm with the identical soliton separation is achieved, including soliton triplet, soliton quartet, and soliton quintet. Additionally, the STML soliton molecule with compound structure can also be obtained, where two different pulse separations exist in the soliton molecule complex, for the inner soliton with the unequal or identical intensity. The transverse mode distributions for different soliton molecule complexes differ from each other, indicating the STML structure of the MM solitons. Our experimental results will extend our further understanding of the spatiotemporal nonlinear dynamics in the MM lasers.

Optical and analytical soliton solutions to higher order non-Kerr nonlinear Schrödinger dynamical model

This article studies the propagation of the short pulse optical model governed by higher order nonlinear Schrödinger equation (HNLSE) with non-Kerr nonlinearity. The model is used to describe the propagation of ultrashort photons in highly nonlinear media. Upon establishing the general framework, we discuss the statics and dynamics of HNLSE by employing an extended modified auxiliary equation mapping (EMAEM) architectonic to obtain some new solitary wave solutions like bright dromion (soliton), domain wall, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. Obtained optical soliton solutions are analysed graphically to represent features like as width, amplitude, and structure of solitons. We will also discuss our governing model for M-shaped, Homoclinic breathers, multiwave, kink cross rational, and interaction of M-shaped with 1 and 2 kink solutions with the help of various ansatz transformations.

Longitudinal-transverse soliton chains analog to heisenberg ferromagnetic spin chains in (2+1) dimensional with biquadrant interactions

In quantum spin systems, lower energy state for a nuclear spin in an external field is spin (+1/2) while the higher energy state is spin (-1/2). A continuum analog to the discrete model led to nonlinear Schrodinger equation (NLSE) with higher order dispersion. Recently, a model equation with bilinear and biquadratic interactions in the (2 + 1) dimensional Heisenberg ferromagnetic spin chain (HFSC), was derived in the literature. This model equation is a NLSE with quartic dispersion and fifth degree nonlinearity, and it was rarely considered in the literature. The, only, work done has shown solitons solutions. This motivated us to consider this problem for inspecting the multiple characteristics of the HFSC in space-time. Here, the exact solutions of the HFSC biquadratic model equation are obtained by using the unified method (UM). In applications, it is found the UM is of low time cost in symbolic computations. So, we think that it prevails the known methods. The solutions obtained are evaluated numerically and shown in figures.These figures reveal that the solutions exhibit longitudinal-transverse (L-T) solitons chains (SCs) with presence (or absence) of tunneling, depending on the values of the parameters of high dispersivity and high nonlinearity. Also, L-T zig-zag SCs are observed, where pulses with higher amplitudes (or gaps) occur along a characteristic line. Furthermore, L-TSCs modulation along the space axes is shown. It is remarked that the contour plots show complex lattice waves, which is relevant to the spin chain system. So, the present work reveals new solitons structures induced by bilinear-biquadratic interactions of HFSC.

Abundant optical soliton structures to the Fokas system arising in monomode optical fibers

Abstract Three effective methods, namely, the simplified extended tanh-function method (SETFM), variational method (VM) and He’s frequency formulation method (HFFM) are employed to investigate the Fokas system that arises in the monomode optical fibers. Fifteen sets of the soliton solutions such as the bright soliton, dark soliton, bright-dark soliton, double-dark soliton, double-bright soliton, triple-bright soliton, kinky periodic soliton and perfect periodic soliton solutions are developed. The dynamic performances of the different soliton solutions are plotted via the 3-D contours and 2-D curves to interpret the physical behaviors by assigning reasonable parameters. From the results obtained from this study, it is found that three proposed methods are promising ways to seek various soliton solutions of the PDEs in optical physics.

On some optical soliton structures to the Lakshmanan-Porsezian-Daniel model with a set of nonlinearities

On some optical soliton structures to the Lakshmanan-Porsezian-Daniel model with a set of nonlinearities

A Study of the Soliton Solutions with an Intrinsic Fractional Discrete Nonlinear Electrical Transmission Line

This study aims to identify soliton structures as an inherent fractional discrete nonlinear electrical transmission lattice. Here, the analysis is founded on the idea that the electrical properties of a capacitor typically contain a non-integer-order time derivative in a realistic system. We construct a non-integer order nonlinear partial differential equation of such voltage dynamics using Kirchhoff’s principles for the model under study. It was discovered that the behavior for newly generated soliton solutions is impacted by both the non-integer-order time derivative and connected parameters. Regardless of structure, the fractional-order alters the propagation velocity of such a voltage wave, thus bringing up a localized framework under low coupling coefficient values. The generalized auxiliary equation method drove us to these solitary structures while employing the modified Riemann–Liouville derivatives and the non-integer order complex transform. As well as addressing sensitivity testing, we also investigate how our model’s altered dynamical framework shows quasi-periodic properties. Some randomly selected solutions are shown graphically for physical interpretation, and conclusions are held at the end.

Rational soliton solutions of nonlocal multicomponent nonlinear Schrödinger equations

In this paper, we present a generalized Darboux transformation for nonlocal multicomponent nonlinear Schrödinger (NLS) equations. Also, we provide a unified formula for Nth-order rational soliton solution of discussed nonlocal multicomponent NLS equations. In particular, the first- and second-order rational soliton solutions of nonlocal three-component NLS equations are obtained. Moreover, we discuss the wave structures of these rational solitons of nonlocal three-component NLS equations with different parameters.

Study of cylindrical and spherical dust acoustic solitons and quasiperiodic structures in a quantum dusty plasma

The solitonic and quasiperiodic structures of dust acoustic (DA) waves are investigated in a three components quantum dusty plasma composed of mobile negative dust grains, ions, and inertialess electrons. The reductive perturbation method is employed to derive A deformed Korteweg–de Vries (dKdV) equation in planar and nonplanar geometries, and its numerical solutions are obtained using the two level finite difference approximation method. The influence of geometries on DA solitons is discussed. It is observed that in nonplanar geometries, DA solitons travel at different speeds in comparison to one-dimensional planar ones. Furthermore, in the planar geometry, the bifurcation of DA traveling waves has been analyzed on the framework of the dKdV equation. By adding an external periodic force to the derived dKdV equation, the quasiperiodic behaviors of DA waves are presented.