Small-amplitude Solitons Research Articles

Propagation of dark solitons of DNLS equations along a large-scale background

We study dynamics of dark solitons in the theory of the derivative nonlinear Schrödinger equations by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes’ remark that relationships for harmonic linear waves and small-amplitude soliton tails satisfy the same linearized equations, so the corresponding solutions can be converted one into the other by replacement of the packet’s wave number k by iκ, κ being the soliton’s inverse half-width, we find the Hamiltonian and the canonical momentum of the soliton’s motion. The Hamilton equations are reduced to the Newton equation whose solutions for some typical situations are compared with exact numerical solutions of the Kaup-Newell DNLS equation.

Nonlinear dynamics of large-amplitude, small-scale Alfvén waves

We study large-amplitude, very oblique Alfvén waves at low β, with small gradient length scales, comparable to the ion inertial scale di. Such waves have large density fluctuations and slight dispersion from finite-frequency and finite-ion sound radius effects. We derive a weakly nonlinear evolution equation governing the behavior of the waves in one dimension and categorize the different solitons appearing in different regimes: the regular solitons involve full rotations of the transverse magnetic field similar to modified Korteweg–de Vries (mKdV) solitons (our nonlinear equation reduces to the mKdV equation in the long-wavelength limit). However, for sufficiently small soliton widths, some become singular, small-amplitude solitons with density discontinuities and, are, thus expected to become strongly dissipative in a real plasma. These solutions may be useful in explaining some aspects of the sharp, ion-scale magnetic field rotations (switchbacks) observed in the near-Sun solar wind by Parker Solar Probe.

Boundary effects on dispersion relations of ion-acoustic wave and physical properties of overlapping soliton in a plasma waveguide

Taking into account the cylindrical boundary, a theoretical investigation has been made for the low frequency electrostatic waves in an electron-positron-ion plasma waveguide. The dispersion relation of ion-acoustic (IA) wave is obtained, and a predication for the linear interaction phenomenon of small-amplitude cylindrical IA solitons is presented. It is shown that the cylindrical boundary has significant effects on the dispersion property of IA waves, and the frequency for short wave is significantly modified by the plasma parameters. It has also been noted that cylindrical IA solitons add up linearly when they overlap and penetrate through each other, the maximum amplitude of the overlapping soliton is nearly the sum of the individual soliton amplitude, indicating an apparent linear interaction. Furthermore, the relationships between phase delay and kinetic energy of colliding solitons for an axisymetric cylindrical geometry are derived and discussed in detail. The work presented would be useful to enrich the solitons interaction theory in astrophysical and laboratorial plasma situations.

Weakly Nonlinear Dust-Ion-Acoustic Solitons in an Electronegative Collisionless Dusty Plasma With Cairns–Gurevich Distributed Electrons

The problem of dust-ion-acoustic (DIA) solitons is addressed in an electronegative collisionless dusty plasma with the presence of trapped-nonthermal electrons. To do this, we revisited the Cairns–Gurevich distribution that describes, concurrently, the evolution of the energetic electrons and those trapped in the plasma potential and analytically expressed its corresponding density. The modifications, due to the presence of this trapped nonthermal density, arising in small-amplitude DIA solitons propagation associated with both space and experimental plasmas are analyzed. In particular, we have found that, in both cases, a proportion of trapped nonthermal electrons relatively significant makes the solitary structure less spiky. Besides, we have shown that the amplitude and width of the experimental plasma soliton seem more affected due to the low ionic mass ratio.

Evolution of ion-acoustic soliton waves in Venus’s ionosphere permeated by the solar wind

Abstract Wave observations are as yet an important technique to resolve fine structures in the plasma that cannot be identified by different instruments. In this way, we proposed the generation of electrostatic solitary waves during the interaction between the solar wind particles and Venus’s atmosphere at high altitude. The plasma system is treated as a multicomponent unmagnetized plasma consists of background electrons, positive ions (H+ and O+), and streaming solar wind electrons and protons. The dispersion relation is derived for linear waves and the stability/instability of electrostatic wavepackets is investigated. The dependence of the instability growth rate on the ion beam speed has been analyzed. Stability analysis reveals the occurrence of an imaginary frequency part in three regions. Using the reductive perturbation theory, the set of fluid equations is reduced to the Korteweg-de Vries (KdV) equation to describe the evolution of small but finite amplitude soliton waves. The model predicts the propagation of electrostatic soliton waves with an electric field of 1.2 mV/m and a time duration of 0.4 ms. The output of the fast Fourier transform of the electric field pulse is a broadband in the frequency range of ~ 3.2 to 199.5 kHz. It is proposed that the model can be a decent possibility for clarifying the observation of a wide variety of plasma oscillations by Galileo flyby of Venus.

Characteristics of nonlinear ion-acoustic waves in collisional plasmas with ionization effects

In this work, we have investigated the linear and nonlinear propagation of ion-acoustic solitary waves in a collisional plasma composed of isothermal warm ions and a population of nonthermal electrons generated from the Kappa, Tsallis, and Cairns distribution. The effects of ionization, ion loss, and ion-neutral collision on ion-acoustic waves are also considered here. The standard reductive perturbation theory has been used to study the small but finite amplitude solitons. It is found that the nonlinear dynamics of the considered system are governed by the damped Korteweg-de Vries (dK-dV) equation. The solution of the damped K-dV equation is analyzed numerically. The effects of the nonthermal parameters, namely , , and on the ion-acoustic wave structures are discussed. Moreover, the effects ionization, ion loss, and ion-neutral collisions on solitary wave structures are also investigated here. It is shown that ionization effects lead to the growth of the IA solitons whereas collisions reduce this growth rate.

Ion‐acoustic solitary waves in e‐p‐i plasmas with (r, q)‐distributed electrons and kappa‐distributed positrons

AbstractIn this paper, we have studied the propagation of non‐linear ion‐acoustic waves in a plasma comprising of (r, q)‐distributed electrons and kappa‐distributed positrons. We have investigated the effect of complete electron distribution profile on the propagation of small, as well as arbitrary, amplitude solitons (via pseudopotential technique) by using generalized (r, q) distribution, which exhibits a spiky and flat top nature at low energies and a super‐thermal tail at high energies. Interestingly, for negative values of r, solitons are formed with both polarities, positive (compressive) and negative (rarefactive), separately within a small amplitude limit and exist simultaneously in an arbitrary amplitude limit. We also found that the propagation of solitons has been affected by the change in parameters r, q, positron concentration, and electron to positron temperature ratio. The results presented in this study add to the fundamental understanding of the complete profile of the electron distribution function, high‐ and low‐energy parts, and in the formation of compressive and rarefactive small and finite amplitude solitons in both space and astrophysical plasmas.

Vector Topological Edge Solitons in Floquet Insulators

We introduce topological vector edge solitons in a Floquet insulator, consisting of two honeycomb arrays of helical waveguides with opposite directions of rotation in a focusing nonlinear optical medium. Zigzag edges of two arrays placed in contact create a zigzag-zigzag interface between two structures with different topology. A characteristic feature of such a photonic insulator is that, in the linear limit, it simultaneously supports two topologically protected chiral edge states at the interface between the two arrays. In the presence of nonlinearity, either bright or dark scalar Floquet edge soliton can bifurcate from a linear topological edge state. Such solitons are unidirectional and are localized in both directions, along the interface due to nonlinear self-action, and across the interface as being an edge state. The presence of two edge states with equal averaged group velocities enables the existence of stable topological vector edge solitons. In our case, these are nonlinearly coupled bright and dark solitons bifurcating from different branches of the topological Floquet edge states. Here we put forward a new mathematical description of scalar and vector small-amplitude Floquet envelope solitons in the above-mentioned continuous system. Importantly for the design of future photonic devices based on Floquet edge solitons, we find that the latter can be described by nonlinear Schrodinger equations for the mode envelopes obtained by averaging over one rotation period in the evolution coordinate.

Nonlinear Dispersive and Dissipative Electrostatic Structures in Two-Dimensional Electron-Positron-Ion Quantum Plasma

The nonlinear features of two-dimensional ion acoustic (IA) solitary and shock structures in a dissipative electron-positron-ion (EPI) quantum plasma are investigated. The dissipation in the system is taken into account by incorporating the kinematic viscosity of ions in plasmas. A quantum hydrodynamic (QHD) model is used to describe the quantum plasma system. The propagation of small but finite amplitude solitons and shocks is governed by the Kadomtsev-Petviashvili-Burger (KPB) equation. It is observed that depending on the values of plasma parameters (viz. quantum diffraction, positron concentration, viscosity), both compressive and rarefactive solitons and shocks are found to exist. Furthermore, the energy of the soliton is computed and possible solutions of the KPB equation are presented numerically in terms of the monotonic and oscillatory shock profiles

Plasma Parameters Effects on Dust Acoustic Solitary Waves in Dusty Plasmas of Four Components

The presence and propagation of dust-acoustic solitary waves in dusty plasma contains four components such as negative and positive dust species beside ions and electrons are studied. Both the ions and electrons distributions are represented applying nonextensive formula. Employing the reductive perturbation method, an evolution equation is derived to describe the small-amplitude dust-acoustic solitons in the considered plasma system. The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. This study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the first-order nonlinear coefficient. The structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. The coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation.

Three-Component Soliton States in Spinor F=1 Bose-Einstein Condensates.

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F=1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

Solitons in -symmetric ladders of optical waveguides

We consider a -symmetric ladder-shaped optical array consisting of a chain of waveguides with gain coupled to a parallel chain of waveguides with loss. All waveguides have the focusing Kerr nonlinearity. The array supports two co-existing solitons, an in-phase and an antiphase one, and each of these can be centred either on a lattice site or midway between two neighbouring sites. We show that both bond-centred (i.e. intersite) solitons are unstable regardless of their amplitudes and parameters of the chain. The site-centred in-phase soliton is stable when its amplitude lies below a threshold that depends on the coupling and gain–loss coefficient. The threshold is lowest when the gain-to-gain and loss-to-loss coupling constant in each chain is close to the interchain gain-to-loss coupling coefficient. The antiphase site-centred soliton in the strongly-coupled chain or in a chain close to the -symmetry breaking point, is stable when its amplitude lies above a critical value and unstable otherwise. The instability growth rate of solitons with small amplitude is exponentially small in this parameter regime; hence the small-amplitude solitons, though unstable, have exponentially long lifetimes. On the other hand, the antiphase soliton in the weakly or moderately coupled chain and away from the -symmetry breaking point, is unstable when its amplitude falls in one or two finite bands. All amplitudes outside those bands are stable.

CPT-symmetric coupler with intermodal dispersion.

A dual-core waveguide with balanced gain and loss in different arms and with intermodal coupling is considered. The system is not invariant under the conventional PT symmetry, but obeys CPT symmetry where an additional spatial inversion C corresponds to swapping the coupler arms. We show that second-order dispersion of coupling allows for unbroken CPT symmetry and supports propagation of stable vector solitons along the coupler. Small-amplitude solitons are found in explicit form. The combined effect of gain-and-loss and dispersive coupling results in several interesting features which include a separation between the components in different arms, nontrivial dependence of stability of a soliton on its velocity, and the existence of more complex stationary two-hump solutions. Unusual decay dynamics of unstable solitons are also discussed.

Ion-acoustic solitary waves in a positron beam plasma with electron trapping and nonextensivity effects

Ion-acoustic solitary waves (IASWs) are investigated in a plasma having a cold positron beam fluid, electrons following a vortex-like distribution with entropic index q, and dynamic ions. Using a standard procedure, a pseudo-potential energy equation is derived. The presence of nonextensive q- distributed trapped electrons and cold positron beam has been shown to influence the small amplitude soliton structure quite significantly. From the analysis of our results, it is shown that compressive IASWs are supported in this plasma model. As the real plasma situations are observed with plasma species having a relative flow, our present analysis should be beneficial for comprehending the electrostatic solitary structures observed in fusion plasma devices and positron winds observed in astrophysical plasmas.

The vortex structure of magnetic solitons

Soliton excitations in the general form are considered using the classical model, in a two-dimensional easy-plane ferromagnet. Equations are derived and solved for small-amplitude two-parameter dynamic solitons. It is demonstrated that they have a vortex structure and that as their amplitude increases, the excitations turn into coupled quadrupole vortex states that are characterized by two dynamic parameters: the soliton velocity and its internal precession frequency. The limit transitions of vortex solitons in the general form into vortex dipoles, magnetic lamps, and magnon droplets, are analyzed. The obtained results are compared against the corresponding information about solitons in one-dimensional magnetic systems.

A small-amplitude study of solitons near critical plasma compositions

The properties of small-amplitude solitons are established near critical plasma compositions in a generalized fluid plasma with an arbitrary number of species. The study is conducted via a Taylor series expansion of the Sagdeev potential. It is shown that there are two types of critical compositions, namely rich critical and poor critical compositions. The coexistence of positive and negative polarity solitons is shown to arise at rich critical compositions and near rich critical compositions. At poor critical compositions, no small-amplitude solitons exist, while weak double layers arise near poor critical compositions. A novel analytical expression is obtained for a small-amplitude acoustic speed soliton solution near rich critical compositions. These solitons have a Lorentzian shape with much fatter tails than regular solitons. A case study is also performed for a simple fluid model consisting of cold ions and two Boltzmann electron species. Exact agreement is obtained between the Sagdeev analysis and reductive perturbation theory. For the first time, we derive the same Lorentzian acoustic speed soliton from reductive perturbation theory.

Nonlinear dynamics of ion acoustic waves in quantum pair-ion plasmas

The nonlinear properties of the ion acoustic waves (IAWs) in a three-component quantum plasma comprising electrons, and positive and negative ions are investigated analytically and numerically by employing the quantum hydrodynamic (QHD) model. The Sagdeev pseudopotential technique is applied to obtain the small-amplitude soliton solution. The effects of the quantum parameter$H$, positive to negative ion density ratio${\it\beta}$and Mach number on the nonlinear structures are investigated. It is found that these factors can significantly modify the properties of the IAWs. The existence of quasi-periodic and chaotic oscillations in the system is established. Switching from quasi-periodic to chaotic is possible with the variation of Mach number or quantum parameter$H$.

A New Approach to Energy Integral for Investigation of Dust—Ion Acoustic (DIA) Waves in Multi-Component Plasmas with Quantum Effects in Inertia Less Electrons

Dust-ion acoustic waves are investigated in this model of plasma consisting of negatively charged dusts, cold ions and inertia less quantum effected electrons with the help of a typical energy integral. In this case, a new technique is applied formulating a differential equation to establish the energy integral in case of multi-component plasmas which is not possible in general. Dust-ion acoustic (DIA) compressive and rarefactive, supersonic and subsonic solitons of various amplitudes are established. The consideration of smaller order nonlinearity in support of the newly established quantum plasma model is observed to generate small amplitude solitons at the decrease of Mach number. The growths of soliton amplitudes and potential depths are found more sensitive to the density of quantum electrons. The small density ratio r(= 1 − f) with a little quantized electrons supplemented by the dust charges Zd and the in-deterministic new quantum parameter C2 are found responsible to finally support the generation of small amplitude solitons admissible for the model.

Interaction of spatially overlapping standing electromagnetic solitons in plasmas

Numerical investigations on mutual interactions between two spatially overlapping standing electromagnetic solitons in a cold unmagnetized plasma are reported. It is found that an initial state comprising of two overlapping standing solitons evolves into different end states, depending on the amplitudes of the two solitons and the phase difference between them. For small amplitude solitons with zero phase difference, we observe the formation of an oscillating bound state whose period depends on their initial separation. These results suggest the existence of a bound state made of two solitons in the relativistic cold plasma fluid model.

Existence domains of arbitrary amplitude nonlinear structures in two-electron temperature space plasmas. I. Low-frequency ion-acoustic solitons

Using the Sagdeev pseudopotential technique, the existence of large amplitude ion-acoustic solitons is investigated for a plasma composed of ions, and hot and cool electrons. Not only are all species treated as adiabatic fluids but the model for which inertial effects of the hot electrons is neglected whilst retaining inertia and pressure for the ions and cool electrons has also been considered. The focus of this investigation has been on identifying the admissible Mach number ranges for large amplitude nonlinear ion-acoustic soliton structures. The lower Mach number limit yields a minimum velocity for the existence of ion-acoustic solitons. The upper Mach number limit for positive potential solitons is found to coincide with the limiting value of the potential (positive) beyond which the ion number density ceases to be real valued, and ion-acoustic solitons can no longer exist. Small amplitude solitons having negative potentials are found to be supported when the temperature of the cool electrons is negligible.