Formation Of Solitons Research Articles

Traveling waves solutions of Hirota–Ramani equation by modified extended direct algebraic method and new extended direct algebraic method

In this paper, new exact traveling wave solutions are obtained by Hirota–Ramani equation. The many exact complex solutions of several types of nonlinear partial differential equations (NPDEs) are presented using the modified extended direct algebraic approach and new extended direct algebraic method, which is among the most effective mathematical techniques for finding a precise solution to NPDEs and put into a framework of algebraic computation. By selecting different bright and solitary soliton forms and by creating various analytical optical soliton solutions for the investigated equation, we hope to demonstrate how the analyzed model’s parameter impacts soliton behavior. It is possible to obtain new, complex solutions for nonlinear equations like the [Formula: see text]-dimensional Hirota–Ramani equation.

Nonlinear-Fourier-Transform-Based Dynamic Analyses on the Multiple Cavity Solitons in Kerr Microresonators

The Kerr microresonators have aroused widespread interests for their ultrahigh integration, compatible fabrication and ultralow energy consumption. Similar to the traditional mode-locked fiber lasers, the microresontors can sustain the generation of dissipative solitons called cavity solitons relying on the double balance of gain and loss as well as nonlinearity and dispersion. The state of multiple solitons is common in the microresonator with anomalous dispersion. In particular, an ideal state named as soliton crystals is obtained when the multiple solitons have a equidistant arrangement. And recent experiments have successfullly observed soliton crystals in the Kerr microresonators. To intuitively reveal the formation and evolution dynamics of the multiple solitons and get insight into the underlying physical mechanisms of soliton crystals, we applied the nonlinear Fourier transform to project these states into nonlinear discrete spectrum. The discrete spectra of single soliton with different modulated background waves have been displayed, which can help distinguish different optical components. Then, the nonlinear spectrum evolution of normal multiple solitons state shows the typical nonlinear states of the intracavity field. And the equidistant solitons have the effects of power enhancement, whose spectral intensity is several times that of a single soliton state. Comparing with the discrete spectrum of the equidistant solitons, the solitons inside the soliton crystals interact with each other by the modulated background. Our results suggest that the nonlinear Fourier transform is a powerful technique to characterize soliton dynamics in the Kerr microresonator, which provides a new perspective to understand the interactions of cavity solitons.

On the spectral sidebands’ evolution of mode-locked fiber lasers

We numerically investigate the role played by small-signal gain, intracavity dispersion, and spectral filtering on spectral sidebands generation and evolution of mode-locked fiber lasers. For a fixed intracavity dispersion, increasing small-signal gain shifts the spectral sidebands toward the central wavelength with enhanced intensities, which results in spectral distortion and soliton pulsation. The wavelength location and intensity of the spectral sidebands can also be manipulated in different operation regimes through the intracavity dispersion variation. On the other hand, spectral filtering significantly influences the soliton pulse formation through the insertion loss and spectral narrowing effects, which affects the properties of the soliton pulses. The obtained experimental results of our proposed mode-locked fiber laser are in consistent with the simulation results achieved from extended vector nonlinear Schrödinger equations.

Dynamics of newly created soliton solutions via Atangana–Baleanu Fractional (ABF) for system of (ISALWs) equations

In this work, newly created soliton solutions for ion sound and Langmuir waves with an Atangana–Baleanu fractional (ABF) are given. Symbolic software is used to perform the unified solver method (USM) and Weierstrass elliptic function method (WEFM) in order to solve this model. In terms of hyperbolic functions, extended trigonometric functions, and so forth. Single-wave solutions that were entirely novel and universal were attained. The way the soliton solutions behaved in connection with the two-dimensional (2D) and three-dimensional (3D) graphics was also investigated. The dynamic investigation of the newly created soliton solutions reveals that they have several soliton forms like single-soliton, bell-shaped and mixed-form soliton profiles. This strategy is viewed as promising for handling a range of ABF evolution systems.

Interplay between intensity-dependent dispersion and Kerr nonlinearity on the soliton formation.

A generalized nonlinear Schrödinger equation is studied with the interplay between Kerr nonlinearity and intensity-dependent dispersion. The supported soliton solutions are characterized analytically in different families by the pseudo-potential method, in terms of Maimistov and Cuspon solitons for different ratio between the intensity-dependent dispersion and Kerr nonlinearity. Direct numerical simulations also agree with our analytical formulas. In addition to the well-studied Kerr-type nonlinearity, our results reveal an unexplored scenario with the introduction of the nonlinear corrections to wave dispersion.

Modulational instability of ion-acoustic waves in a dense quantum plasma

Modulational instability of ion-acoustic (IA) waves is investigated in an unmagnetized quantum plasma by adopting an equation of state for Fermi electron gas. To this end, a basic set of one-dimensional quantum hydrodynamic equations is reduced to a nonlinear Schrödinger equation using the reductive perturbation method. Quantum corrections are described using a nondimensional quantum parameter H proportional to the quantum diffraction parameter. Based on normalized electron temperature and chemical potential, new quantum criteria of modulational instability for IA waves are obtained and analyzed. Moreover, formation of rogue waves due to the modulational instability of IA waves and propagation of modulated IA packets in the form of bright and dark envelope solitons are examined for two different types of astrophysical plasma regions: white dwarf stars and warm dense matter.

Nucleation of transition waves via collisions of elastic vector solitons

In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multistable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from colliding waves, and we numerically investigate head-on and overtaking collisions of solitary waves with vectorial properties (i.e., elastic vector solitons). Unlike KdV-type solitons, which maintain their shape despite collisions, our system shows that collisions of two vector solitons can cause nucleation of a new phase via annihilation of the vector solitons, triggering the propagation of transition waves. The propagation of these depends both on the amount of energy carried by the vector solitons and on their respective rotational directions. The observation of the initiation of transition waves with collisions of vector solitons in multistable mechanical systems is an unexplored area of fundamental nonlinear wave interactions and could also prove useful in applications involving reconfigurable structures.

Mere tension output from spring-linkage-based mechanical metamaterials.

Metamaterials whose properties are inaccessible with conventional materials offer powerful tools for unprecedentedly manipulating physical signals. However, an effective design strategy of metamaterials still remains a challenge for changing the compression or tension characters of stress waves during forward propagation. Here, we introduce a class of spring-linkage-based metamaterials exhibiting mere tension output at the distal end, no matter that the input is an axial impact, a sudden tension, or even alternating tension-compression. The metamaterials can turn compressive waves into pure tension and filter them out from the tension-compression mixed ones while allowing tensile signal stably propagating in soliton form. This is achieved by combining nonuniform and nonlinear properties of the proposed cells. In particular, these extraordinary functions of the metamaterial can be turned on or off and adjusted by tuning a key switch cell; thus, it is anticipated to serve as a start for more complex manipulation and utilization of mechanical signals.

Transient dynamics of dissipative solitons formation in a net-normal dispersion mode-locked fiber laser based on nonlinear polarization evolution.

In mode-locked fiber lasers, the formation of ultrashort pulses from noisy or unstable states is a crucial area of research. Investigating these complex nonlinear dynamics can lead to valuable insights and new practical engineering techniques, particularly for the design and optimization of optical systems. Time-stretch dispersive Fourier transform, utilized in our study to investigate dissipative solitons formation in a net-normal dispersion nonlinear polarization evolution mode-locked fiber laser, provides a window into the intricate dynamics of such systems. In our experiments, the identification of five distinct transient stages in the formation process sheds light on the underlying mechanisms of dissipative soliton (DS) formation. The five distinct transient stages involved in the formation process include relaxation oscillation, modulation instability, spectral broadening, soliton explosions (SEs), and stable mode-locking. Notably, we also observed the generation of dissipative rogue waves during the SE stage. Our findings shed light on the intricate dynamics of DS formation and offer valuable insights for the design and optimization of mode-locked fiber lasers.

AlGaAs soliton microcombs at room temperature.

Soliton mode locking in high-Q microcavities provides a way to integrate frequency comb systems. Among material platforms, AlGaAs has one of the largest optical nonlinearity coefficients, and is advantageous for low-pump-threshold comb generation. However, AlGaAs also has a very large thermo-optic effect that destabilizes soliton formation, and femtosecond soliton pulse generation has only been possible at cryogenic temperatures. Here, soliton generation in AlGaAs microresonators at room temperature is reported for the first time, to the best of our knowledge. The destabilizing thermo-optic effect is shown to instead provide stability in the high-repetition-rate soliton regime (corresponding to a large, normalized second-order dispersion parameter D2/κ). Single soliton and soliton crystal generation with sub-milliwatt optical pump power are demonstrated. The generality of this approach is verified in a high-Q silica microtoroid where manual tuning into the soliton regime is demonstrated. Besides the advantages of large optical nonlinearity, these AlGaAs devices are natural candidates for integration with semiconductor pump lasers. Furthermore, the approach should generalize to any high-Q resonator material platform.

Genetic-Algorithm-Based Design of Large-Mode- Area All-Solid Anti-Resonant Fiber With Normal Dispersion and Single-Mode Operation in the 2 μm Wavelength Region

Recent years have witnessed much progress in the development of fiber lasers in the 2 μm region. Yet, to date, their power levels are limited by modulation instability and soliton formation attributed to the strong anomalous dispersions of fused silica in this wavelength region. Further power scaling requires a novel design of an all-solid silica active fiber that features normal dispersion by compensating the material dispersion with the waveguide dispersion. At the same time, a large mode area, low losses, single mode operation and robustness need to be maintained. In this paper, we propose an all-solid anti-resonant fiber (AS-ARF) design that meets these demands. We demonstrate that normal dispersion can be achieved in AS-ARFs at 2 μm by exploiting the Kramers-Kronig relation. To balance the desired dispersion with the other performance parameters, we optimize the design of the AS-ARFs using a genetic algorithm. The optimized AS-ARF has a mode field area of 1170 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and normal dispersion over the spectrum from 1.96 μm to 2.04 μm. Within this spectrum, the maximum confinement loss (CL) of the fundamental mode (FM) is 16 dB/km and the minimum CL of the higher order modes (HOMs) is over 100 dB/km. The HOMs can be easily coupled out by bending the fiber while the FM stays in the core. For example, the CLs are over 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> dB/km for the HOMs and below 200 dB/km for the FM at 2 μm at a bending radius of 20 cm. Moreover, the properties of the proposed AS-ARF remain favorable even under large geometric variations, showing good tolerance to manufacturing errors. We expect the proposed AS-ARF to further stimulate the development of high-power fiber lasers in the 2 μm region.

Robust Multimode Waveguide Design for Avoided Mode Crossing-Suppressed Microresonators

Microresonator-based optical frequency combs enable many potential applications, from frequency metrology to optical communication. Soliton comb generation relies on dispersion control. For bright soliton generation, it is required to have anomalous group velocity dispersion. However, the avoided mode crossing in the microresonator can disturb the local dispersion and may prevent the soliton formation. Although the avoided mode crossing may enable dark soliton generation, the unintended avoided mode crossing distorts the comb spectrum. Here, we present a robust multimode waveguide design against intermodal coupling to suppress unintended avoided mode crossing. By engineering the waveguide dimension, the phase mismatch between coupling modes can be increased, which will significantly reduce the modal coupling strength. We experimentally demonstrated the avoided mode crossing-suppressed microresonators in the AlGaAs-on-insulator platform.

Vortex solitons in moiré optical lattices.

We show that optical moiré lattices enable the existence of vortex solitons of different types in self-focusing Kerr media. We address the properties of such states both in lattices having commensurate and incommensurate geometries (i.e., constructed with Pythagorean and non-Pythagorean twist angles, respectively), in the different regimes that occur below and above the localization-delocalization transition. We find that the threshold power required for the formation of vortex solitons strongly depends on the twist angle and, also, that the families of solitons exhibit intervals where their power is a nearly linear function of the propagation constant and they exhibit a strong stability. Also, in the incommensurate phase above the localization-delocalization transition, we found stable embedded vortex solitons whose propagation constants belong to the linear spectral domain of the system.

Formation of multi-peak gap solitons and stable excitations for double-Lévy-index and mixed fractional NLS equations with optical lattice potentials

In this paper, we investigate the new two-Lévy-index fractional nonlinear Schrödinger (FNLS) equations with optical lattices, where two fractional derivative terms are introduced to control the diffractions. Especially, we explore the linear Bloch bandgaps and existence of gap solitons for the two-Lévy-index mixed FNLS equations with optical lattices. We analyse the effects of different coefficients of normal and abnormal diffraction terms on bandgap structures. Families of single-, double-, triple-, as well as quadruple-peak solitons are found in the first gap with the defocusing nonlinearity while such solitons can be found in the semi-infinite gap when it turns to the focusing regime. Meanwhile, we find that the above-obtained gap solitons can be roughly divided into two types, one of which branches out from the band edge, and another one cannot branch out from the band edge. Moreover, the stability of gap solitons is discussed via the linear stability analysis, and then their dynamical behaviours are verified by means of direct simulations. And stable multi-peak solitons can be obtained via analysing the phase structure. Meanwhile, we find the stable excitations of gap solitons via excitations of system parameters. The stable gap solitons are also verified to appear in the two-Lévy-index FNLS equation. These results may pave the way for the study of linear and nonlinear phenomena of two-Lévy-index and mixed FNLS equations or other mixed fractional physical models in optical lattices and the related physical experimental designs.

Effect of Variable Dust Charge on Overtaking Collision of Multi-Solitons in Dusty Plasma

Abstract: The propagation and overtaking collision of dust acoustic multi-soliton in a dusty plasma consisting of kappa-distributed electrons, Boltzmann-distributed ions, and negatively charged dust grains has been investigated. In the Theoretical study, we use the reductive perturbation method to derive the Korteweg–De Vries (KdV) equation. Using the Hirota bilinear method, we have found four-soliton and five-soliton solutions of the KdV equation. It is observed that the dust charge variation coefficients are significantly affected by the spectral indices of the electrons. We discovered that plasma systems with variable-charged dust grains support the formation of solitons with greater amplitude. Our results help understanding the nonlinear phenomena that form in the magnetospheres of Saturn and Comet Halley as well as in interstellar dusty plasma. Keywords: Dusty plasma, Overtaking collision, Dust charge variation, Korteweg–De Vries (KdV) equation, Hirota bilinear method.

Interplay of reorientational and thermal solitons: unveiling the dynamic coexistence and enhanced nonlinear response in nematic liquid crystals

Spatial solitons in nematic liquid crystals (NLC) are optical beams that maintain their transverse profile due to the self-focusing effect of light. The mechanism leading to the formation of solitons can be either light-induced reorientation of the elongated molecules or thermal changes in the refractive index induced by a light beam. The specific optical properties of nematic liquid crystals cause the reorientational and thermal solitons to coexist in NLC, and their mutual competition can lead to a reduction or enhancement of the overall nonlinear response of the NLC. The study of the interplay between reorientational and thermal solitons allows a better understanding of the conditions under which the solitons can coexist, compete, or enhance each other. Here, we show that the simultaneous existence of both soliton types can lead to a more robust and versatile nonlinear response and can be used in competitive and synergistic configurations by carefully controlling the temperature, intensity, and polarization of the propagating light. As a result of our experimental findings, it may be possible to shape the nature of the interplay between reorientational and thermal solitons and better understand the behavior of reorientational solitons under varying thermal conditions. Furthermore, understanding this mutual interplay may provide insights into the potential of advanced NLC-based photonic devices that exploit the joint effect of reorientational and thermal nonlinearities.

Tunable optical nonlinearities and surface plasmon resonance in Fe3O4 nanoparticles-decorated Ti3C2 MXene composite for ultrafast fiber lasers

In this work, the Ti3C2 MXene was modified with Fe3O4 nanoparticles to obtain a composite with in-plane optical anisotropy and surface plasmon properties. Based on a side-polished D-shaped fiber (DSF), this Fe3O4/Ti3C2 MXene (F/M) composite exhibits a tunable nonlinear optical (NLO) absorption response under 1.5 μm laser excitation with different polarization states. The modulation depths can be obtained from 0.9% to 12.1%. As an application, the ultrafast erbium-doped fiber laser (EDFL) with multiple pulsed laser operations was demonstrated using the F/M-DSF device as a saturable absorber (SA). Both stable Q-switching and mode-locking operations were demonstrated in the same all-fiber laser cavity, which generated pulsed laser with microsecond and sub-picosecond durations respectively. In addition, the bound state (BS) of solitons in harmonic mode-locked lasers with the pulse time interval of 3 ps and the highest order of 30th was also realized. This versatile and simple-structured all-fiber laser has great potential in various applications, such as optical communication. With the numerical simulations, the dynamic of F/M composite-based soliton mode-locking was also explored, illustrating the mechanism of soliton formation and propagation. This work not only expands the advanced applications of F/M composite in ultrafast photonics but also provides a new perspective for designing and optimizing its ultrafast modulating performance.

Variable coefficient exact solution of Sharma–Tasso–Olver model by enhanced modified simple equation method

This article presents variable coefficients solution in the form of soliton, bell shape solution, periodic solution, parabolic periodic soliton of Sharma–Tasso–Olver equation which fundamentally apply to the fission and fusion mechanism of particle in nuclear physics. Solitary wave takes the leading position in electromagnetic field, atomic quantum theory, theoretical relativistic relation etc. The enhanced modified simple equation (EMSE) method is used to generalize solitary wave solutions for Sharma–Tasso–Olver (STO) equation. The computational software maple 18 is used to derive the corresponding results in the 3D plot, density plot and counter plots for the different types of time function used in EMSE scheme.

Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique.

Nonlinear fractional partial differential equations are highly applicable for representing a wide variety of features in engineering and research, such as shallow-water, oceanography, fluid dynamics, acoustics, plasma physics, optical fiber system, turbulence, nonlinear biological systems, and control theory. In this research, we chose to construct some new closed form solutions of traveling wave of fractional order nonlinear coupled type Boussinesq-Burger (BB) and coupled type Boussinesq equations. In beachside ocean and coastal engineering, the suggested equations are frequently used to explain the spread of shallow-water waves, depict the propagation of waves through dissipative and nonlinear media, and appears during the investigation of the flow of fluid within a dynamic system. The subsidiary extended tanh-function technique for the suggested equations is solved for achieve new results by conformable derivatives. The fractional order differential transform was used to simplify the solution process by converting fractional differential equations to ordinary type differential equations by using the mentioned method. Using this technique, some applicable wave forms of solitons like bell type, kink type, singular kink, multiple kink, periodic wave, and many other types solution were accomplished, and we express our achieve solutions by 3D, contour, list point, and vector plots by using mathematical software such as MATHEMATICA to express the physical sketch much more clearly. Moreover, we assured that the suggested technique is more reliable, pragmatic, and dependable, that also explore more general exact solutions of close form traveling waves.

Adiabatic theory of one-dimensional curved polariton waveguides

We construct a general theory of adiabatic propagation of spinor exciton polaritons in waveguides of arbitrary shape, accounting for the effects of TE-TM splitting in linear polarizations and Zeeman splitting in circular polarizations. The developed theory is applied for the description of waveguides of periodically curved shape. We show that in this geometry the periodic rotation of the effective in-plane magnetic field produced by TE-TM interaction results in a nontrivial band-gap structure, which can be additionally tuned by application of an external magnetic field. It is also demonstrated that spin-dependent interactions between polaritons lead to the formation of stable gap solitons.