Soliton Systems Research Articles

Mixed soliton solutions for the (2+1)-dimensional generalized breaking soliton system via new analytical mathematical method

In this research, we study the dispersive phenomena for the (2+1)-dimensional generalized breaking soliton system (GBSS), which describe the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. The constructed solitary wave results for the (2+1)-dimensional GBSS via extended modified rational expansion (EMRE) method in the form of rational, elliptic, and trigonometric functions including mixed solitons, single bright and dark solitions, combined bright and dark solitons, kink and anti-kink wave solitions, traveling waves, and periodic waves. The physical phenomena of demonstrated results represented by higher dimensional and contour plots graphically with the help of symbolic computation. The obtained results are very helpful in the study of interaction phenomena in fiber optics, mathematical physics, fluid dynamics, geophysics, engineering and many other various areas of scientific fields.

From chaos to stability in soliton mode-locked fibre laser system

Intracavity energy rate in a soliton mode-locked fibre laser is derived by solving the Haus master equation. The influence of net gain, absorber response, saturation energy, nonlinearity and absorption are investigated on stable/unstable states. Intracavity modes include the zeroth, first and higher order solitons. Accordingly, chaotic regime as well as breather modes is recognized as a conventional intracavity state. However, tuning the control parameters also results in a reverse bifurcation and thus returning to a stable state. Accordingly, a chaos-based encryption/decryption system is proposed taking the advantage of using a single-side control process; both the encryption and decryption procedures can be achieved by one of the actions of increasing/decreasing the control parameters.

Coherent Soliton States Hidden in Phase Space and Stabilized by Gravitational Incoherent Structures.

We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for gravitational interactions. We unveil a previously unrecognized regime: By increasing the nonlinearity, the system self-organizes into an incoherent localized structure that contains "hidden" coherent soliton states. The solitons are hidden in the sense that they are fully immersed in random wave fluctuations: The radius of the soliton is much larger than the correlation radius of the incoherent fluctuations, while its peak amplitude is of the same order of such fluctuations. Accordingly, the solitons can hardly be identified in the usual spatial or spectral domains, while their existence is clearly unveiled in the phase-space representation. Our multiscale theory based on coupled coherent-incoherent wave turbulence formalisms reveals that the hidden solitons are stabilized and trapped by the incoherent localized structure. Furthermore, hidden binary soliton systems are identified numerically and described theoretically. The regime of hidden solitons is of potential interest for self-gravitating Boson models of "fuzzy" dark matter. It also sheds new light on the quantum-to-classical correspondence with gravitational interactions. The hidden solitons can be observed in nonlocal nonlinear optics experiments through the measurement of the spatial spectrogram.

A pulse amplitude modulation scheme based on in-line semiconductor optical amplifiers (SOAs) for optical soliton systems

<p>The objective of this work is to simulate a pulse amplitude modulation (PAM) scheme based on in-line semiconductor optical amplifiers for optical soliton systems. The max. power for soliton systems, based on various bits/symbol PAM modulation schemes after a fiber length of 100 km, is simulated and clarified. In addition to the max. Q factor for soliton systems, PAM modulation schemes with various in-line SOA injection currents and a fiber length of 100 km are also simulated and demonstrated in the results. The total electrical power after photo-detectors for soliton systems, based on PAM modulation schemes with various in-line SOA injection currents and a fiber length of 100 km, is also simulated and clarified in the results. The study emphasizes that the higher the SOA injection current, the higher the electrical power and the lower the Q factor that can be achieved in the soliton system.</p>

Radially and azimuthally excited states of a soliton system of vortex and Q-ball

In the present paper, we continue to study the two-dimensional soliton system that is composed of vortex and Q-ball components interacting with each other through an Abelian gauge field. This vortex-Q-ball system is electrically neutral as a whole, nevertheless it possesses a nonzero electric field. Moreover, the vortex-Q-ball system has a quantized magnetic flux and a nonzero angular momentum, and combines properties of topological and nontopological solitons. We investigate radially and azimuthally excited states of the vortex-Q-ball system along with the unexcited vortex-Q-ball system at different values of gauge coupling constants. We also ascertain the behaviour of the vortex-Q-ball system in several extreme regimes, including thin-wall and thick-wall regimes.

Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation

Abstract In this article, the Lie group of transformation method via one-dimensional optimal system is proposed to obtain some more exact solutions of the (4+1)-dimensional Fokas equation. Lie infinitesimal generators, possible vector fields, and their commutative and adjoint relations are presented by employing the Lie symmetry method. An optimal system of the one-dimensional subalgebras is also constructed using Lie vectors. Meanwhile, based on the optimal system, Lie symmetry reductions of the Fokas equation is obtained. A repeated process of Lie symmetry reductions, using the single, double, triple, quadruple, and quintuple combinations between the considered vectors, transforms the Fokas equation into nonlinear ordinary differential equations which produce abundant group-invariant solutions. The same problem was studied by Sadat et al. (Chaos Solitons Fractals 140:110134, 2020) using the same Lie symmetry technique via commutative product approach but with the less number of vector fields and therefore could obtain only three exact solutions as compared to the number of analytic solutions in this paper. In order to provide rich localized structures, some solutions are supplemented via numerical simulation, which produces some breather-type solitons, oscillating multi-solitons on the parabolic-shaped surface, fractal dromions, lump-type solitons, and annihilation of different parabolic multi-solitons profiles. The dynamical behaviors of excitation-localized structures are demonstrated graphically via 3D plots for suitable values of the arbitrary free parameters and independent arbitrary functions.

Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients* *The first author, EK dedicates this work to the memory of his Father-in-law, His Majesty Sado Jean Le Prince, Deceased on the June 2nd, 2020

In this work, we consider the generalized cubic–quintic dissipative Gross–Pitaevskii equation, which governs the dynamics of matter wave solitons in Bose–Einstein condensates with two- and three-body interatomic interactions in a spatiotemporal-dependent dissipative potential consisting of parabolic, linear, and complex terms. By using the ansatz method, the modulational instability and gray, kink, and bright soliton solutions are presented under certain parametric conditions. We found that the complex potential, related to the feeding or the loss of atoms by the condensates seriously modifies the instability and stability domain, while the linear potential has not effect on the stability of the system. With the use of exact analytical soliton-like solutions, we investigate analytically the solitons control system, and the results show that the soliton control system may relax the limitations to parametric conditions. We found that the motion of matter wave solitons in the systems can be manipulated by controlling both the external harmonic and linear trapping potentials. We have established that the amplitude of the matter wave solitons keep no change in propagating in the system though the total number of the condensate atoms decreases (increases) when the condensate losses (gains) atoms. We also showed that the three-body interatomic interactions is responsible of the soliton compression. Our results also revealed that the found exact soliton-like solutions can be used to describe the compression of matter wave solitons in BEC system with loss of atoms.

Transition from bird to butterfly shaped nonautonomous soliton and soliton switching in erbium doped resonant fiber

Through theoretical approach, two soliton solutions for nonautonomous inhomogeneous nonlinear Schrödinger - Maxwell Bloch (INLS-MB) equation is attained with the aid of Darboux transformation technique. Based on obtained solutions, bird and butterfly like wave pattern are attained for the specific choice of inhomogeneous coefficients. Especially, by means of dispersion management scheme, exponential profile is adopted for the dispersion coefficient in the governing two soliton solutions. Also, through the appropriate choices of control parameters in inhomogeneous function, the transition from bird shaped to butterfly shaped pulse is observed astoundingly. Finally, nonautonomous soliton switching achieved through soliton fission and fusion phenomenon which could be observed via properly manipulating dispersion and nonlinearity parameters. The obtained analytical results and graphical illustrations are may helpful for the design of soliton control system in fiber optic communication and soliton based optical switching.

Performance analysis of Q-factor on wavelengths and bit rates using optical solitons with dispersion management

In this paper, the dispersion management using soliton pulses in optical communication system is studied. The performance of the system with and without soliton parameters in terms of Q-factor, BER, and eye diagram is also studied. The proposed system with soliton parameters provides an improvement in Q-factor value by 82.1118 dB compared to that without soliton parameters at bit rate of 20 Gbps at a wavelength of 1550 nm with minimum BER of 0. Thus, soliton pulse can be transmitted dispersion free over optical fiber due to the exact compensation between nonlinearity and group velocity dispersion. The impact of wavelengths and bit rates for the soliton system on Q-factor, BER, and eye height is also investigated. The analysis of the simulation results provides that the values of Q-factor and eye height are inversely proportional to wavelength and proportional to bit rates in the proposed system with soliton parameters. Besides, it is proposed that the soliton pulse is best suited for long-range communication system with dispersion management.

Propagation properties of chirped optical similaritons with dual-power law nonlinearity

Abstract We study the transmission of femtosecond light waves in an inhomogeneous dual-power law nonlinear model under the influence of self-frequency shift effect. Pulse evolution in such system is described by a generalized higher-order nonlinear Schrodinger equation incorporating the contributions of distributed self-frequency shift, dispersion, dual-power law nonlinearity, and gain/loss. As a result, a variety of analytical similaritons are derived for the first time by a similarity transformation connected to the related constant-coefficients model. We found that in the presence of self-frequency shift effect, the optical similaritons acquire a nonlinear chirp which has a power-law dependence on the intensity of the pulse. The evolution behaviors of presented chirped similaritons are also presented in two different soliton control systems.

Stabilization of one-dimensional Townes solitons by spin-orbit coupling in a dual-core system

It was recently demonstrated that 2D Townes solitons (TSs) in two-component systems with cubic self-focusing, which are normally made unstable by the critical collapse, can be stabilized by linear spin-orbit coupling (SOC), in Bose-Einstein condensates and optics alike. We demonstrate that 1D TSs, realized as optical spatial solitons in a planar dual-core waveguide with dominant quintic self-focusing, may be stabilized by SOC-like terms emulated by obliquity of the coupling between cores of the waveguide. Thus, SOC offers a universal mechanism for the stabilization of (quasi-) TSs. A combination of systematic numerical considerations and analytical approximations identifies a vast stability area for skew-symmetric solitons in the system’s main (semi-infinite) and annex (finite) bandgaps. Tilted (”moving”) solitons are unstable, spontaneously evolving into robust breathers. For broad solitons, diffraction, represented by second derivatives in the system, may be neglected, leading to a simplified model with a finite bandgap. It is populated by skew-antisymmetric gap solitons, which are nearly stable close to the gap’s bottom.

Effect of OPC on Fiber Nonlinearities for Dense Soliton Optical Communication Medium

Abstract This review paper scrutinizes the staging of dense wavelength division multiplexing soliton system in return to zero and non-return to zero format. In-line optical phase conjugator (OPC) is used to depreciate the power of four wave mixing (FWM). Destructive interference between both the halves of in-line OPC plummets the FWM power sturdily. This paper concludes with the indication that return-to-zero with OPC gives out better performance with FWM suppression.

Dispersive Fourier transform characterization of multipulse dissipative soliton complexes in a mode-locked soliton-similariton laser

We use the dispersive Fourier transform to spectrally characterize “multipulse soliton complexes” in a dissipative soliton fiber laser operating in the soliton-similariton regime. These multipulse complexes consist of two or more circulating dissipative solitons of picosecond duration, but with temporal separations of ∼5–40 ns, three orders of magnitude greater than the individual pulse durations. The results we present include a multipulse complex of 9 distinct single soliton pulses with ∼10 ns separation, as well as a multipulse complex where a soliton molecule of two bound pulses separated by ∼40 ps coexists with multiple single pulses with separations of ∼30 ns. We also use the dispersive Fourier transform to characterize breathing and transition dynamics in this multipulse regime, and our results add further to the experimental characterization of the diverse range of nonlinear structures in dissipative soliton systems.

Generation and pulsating behaviors of loosely bound solitons in a passively mode-locked fiber laser

We demonstrate the experimental observation of loosely bound solitons and pulsations in a passively mode-locked fiber laser. The soliton amount inside one soliton bunch typically increases with the increment of pump power, while the average pulse-to-pulse separation in the regime of hundreds of picoseconds decreases in principle accordingly. Besides, by employing the real-time measurement based on the dispersive Fourier-transform technique, we find that some solitons in a single bunch are experiencing a simultaneous pulsating process with a period corresponding to 100 times longer than the cavity round-trip time. The experimental results can be beneficial for better understanding the formation of multiple solitons and pulsating solitons and enriching the nonlinear phenomena in complex soliton systems.

Common Hirota form Bäcklund transformation for the unified Soliton system

We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) ≅ GL(2, ) ≅ Möbius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we construct the N-soliton solutions through the KdV type Bäcklund transformation, we can transform different KdV/mKdV/sinh-Gordon equations and the Bäcklund transformations of the standard form into the same common Hirota form and the same common Bäcklund transformation except the equation which has the time-derivative term. The difference is only the time-dependence and the main structure of the N-soliton solutions has the same common form for KdV/mKdV/sinh-Gordon systems. Then the N-soliton solutions for the sinh-Gordon equation is obtained just by the replacement from KdV/mKdV N-soliton solutions. We also give general addition formulae coming from the KdV type Bäcklund transformation which plays not only an important role to construct the trigonometric/hyperbolic N-soliton solutions but also an essential role to construct the elliptic N-soliton solutions. In contrast to the KdV type Bäcklund transformation, the well-known mKdV/sinh-Gordon type Bäcklund transformation gives the non-cyclic symmetric N-soliton solutions. We give an explicit non-cyclic symmetric 3-soliton solution for KdV/mKdV/sinh-Gordon equations.

Rogue waves and analogies in optics and oceanography

We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review state-of-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We conclude with a discussion of important future research directions.

One-dimensional soliton system of gauged kink and Q-ball

In the present paper, we consider a (1 + 1)-dimensional gauge model consisting of two complex scalar fields interacting with each other through an Abelian gauge field. When the model’s gauge coupling constants are set to zero, the model possesses non-gauged Q-ball and kink solutions that do not interact with each other. It is shown here that for nonzero gauge coupling constants, the model has a soliton solution describing the system that consists of interacting Q-ball and kink components. These two components of the kink-Q-ball system have opposite electric charges, meaning that the total electric charge of the system vanishes. The properties of the kink-Q-ball system are studied both analytically and numerically. In particular, it was found that the system possesses a nonzero electric field and is unstable with respect to small perturbations in the fields.

Self-starting bi-chromatic LiNbO3 soliton microcomb

For its many useful properties, including second and third-order optical nonlinearity as well as electro-optic control, lithium niobate is considered an important potential microcomb material. Here, a soliton microcomb is demonstrated in a monolithic high-Q lithium niobate resonator. Besides the demonstration of soliton mode locking, the photorefractive effect enables mode locking to self-start and soliton switching to occur bi-directionally. Second-harmonic generation of the soliton spectrum is also observed, an essential step for comb self-referencing. The Raman shock time constant of lithium niobate is also determined by measurement of soliton self-frequency-shift. Besides the considerable technical simplification provided by a self-starting soliton system, these demonstrations, together with the electro-optic and piezoelectric properties of lithium niobate, open the door to a multi-functional microcomb providing f-2f generation and fast electrical control of optical frequency and repetition rate, all of which are critical in applications including time keeping, frequency synthesis/division, spectroscopy and signal generation.

Evolution of breathers and interaction between high-order lump solutions and N-solitons (N → ∞) for Breaking Soliton system

By employing the Hirota's bilinear method and different test functions, we investigate different forms of breather solitons and some new lump solutions of the (2+1)-dimensional Breaking Soliton system. During this process, some new nonlinear phenomena, such as degeneration of breather solitons, evolution of double breathers and emergence of lump solutions, are studied and shown. Besides, some interaction solutions between high-order lump solutions and N-soliton solutions (N→∞) are studied. We construct the existence theorem of the interaction solutions and give a detailed proof process for the first time. Some different types of interaction solutions are used as concrete examples to illustrate the effectiveness of the described theorem, such as rational-exponential type, rational-cosh-cos type, rational-logarithmic type, and some three-dimensional spatial structure figures are simulated and displayed to reflect the evolutionary behavior of the interaction solutions with the increase of soliton number N.

Improving Soliton Transmission Systems Through Soliton Interactions

Nonlinear interactions between neighboring pulses has always been a fundamental bottleneck in soliton transmission systems. Recently, coherent transceivers, digital signal processing (DSP) and the new nonlinear Fourier transform (NFT) theoretical framework has revived and generalized the field of soliton transmissions into nonlinear frequency division multiplexing (NFDM). We hereby demonstrate analytically and experimentally that one can considerably improve soliton transmission performance by intentionally allowing neighboring solitons to interact and collide during propagation and exchange positions at the receiver followed by standard NFT processing. This can be achieved by designing neighboring solitons' eigenvalues λ to have opposite signs in the real part while the magnitude |R(λ)| is optimized for a given transmission distance so that neighboring transmitted pulses would have swapped their timing positions at the receiver. Experimental results for 6.13 Gbaud 1-soliton systems demonstrate a transmission reach improvement of 100% for 16APSK and 60% for 8PSK modulated on the b-coefficients. The proposed scheme eliminated a long-standing fundamental limitation in soliton transmissions, opened up new dimensions in transmitter signal design and receiver signal processing for nonlinear optical communication systems.