Formation Of Solitons Research Articles

Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes

We study analytically and numerically a frequency downshifting due to power-type frequency-dependent decay of surface waves in the ocean covered by ice floes. The downshifting is obtained both within the linear model and within the nonlinear Schrödinger (NLS) equation augmented by viscous terms for the initial condition in the form of an NLS envelope soliton. It is shown that the frequency-dependent dissipation produces a more substantial downshifting when the spectrum is relatively wide. As a result, the nonlinear adiabatic scenario of wavetrain evolution provides a downshifting remarkably smaller in magnitude than in the linear regime. Meanwhile, interactions between nonlinear wavegroups lead to spectral broadening and, thus, result in fast substantial frequency downshifts. Analytic estimates are obtained for an arbitrary power n of the dependence of a dissipation rate on frequency ∼ωn. The developed theory is validated by the numerical modeling of the generalized NLS equation with dissipative terms. Estimates of frequency downshift are given for oceanic waves of realistic parameters.

Exploring exact solutions for physical differential models through generalized derivatives

In this study, we develop three well-known fractional differential physical models with novel exact solutions. Liouville, Dodd-Bullough-Mikhailov (DBM), and Sinh-Gordon equations are the models under consideration. These models will be broken down into three nonlinear ordinary differential equations using a waveform transformation, which can be precisely solved using the approach of the simplest equation method. The suggested method is applicable to several categories of nonlinear physical models and allows us to extract numerous generalized solutions in soliton and periodic forms The resulting solutions may also be directly compared with a number of findings obtained in the literature. Additionally, representations in two and three dimensions are provided to show how changing the fractional parameter’s amount may impact how monotonic the solutions are obtained.

Optimizing auxiliary laser heating for Kerr soliton microcomb generation.

Auxiliary laser heating has become a widely adopted method for Kerr soliton frequency comb generation in optical microcavities, thanks to its reliable and easy-to-achieve merits for solving the thermal instability during the formation of dissipative Kerr solitons. Here, we conduct optimization of auxiliary laser heating by leveraging the distinct loss and absorption characteristics of different longitudinal and polarization cavity modes. We show that even if the auxiliary and pump lasers enter orthogonal polarization modes, their mutual photothermal balance can be efficient enough to maintain a cavity thermal equilibrium as the pump laser enters the red-detuning soliton regime, and by choosing the most suitable resonance for the auxiliary and pump lasers, the auxiliary laser power can be reduced to 20% of the pump laser and still be capable of warranting soliton generation. Moreover, we demonstrate soliton comb generation using integrated laser modules with a few milliwatt on-chip pump and auxiliary powers, showcasing the potential for further chip integration of the auxiliary laser heating method.

Neutral delay differential equationmodel of an optically injected Kerr cavity.

A neutral delay differential equation(NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second- and higher-order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the low dissipation limit, where the model can be reduced to the Lugiato-Lefever equation(LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE, the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.

Influence on the soliton of changes in the nonlinearity coefficient of the medium

The problem of solitons propagation (electromagnetic waves in the form of solitons) in a medium with a varying nonlinearity coefficient along the propagation trajectory is considered. Сonducted research have shown that the changes occur in the width and amplitude of the soliton while maintaining its energy, with a change in the nonlinearity coefficient of the medium. It is shown that with a sharp change in the nonlinearity coefficient, the soliton is partially destroyed and part of its energy is emitted, i.e. dissipated by the medium. It is shown that an increase in the nonlinearity coefficient leads to a noticeable increase in the amplitude of the soliton with a simultaneous decrease in its width.

Formation of solitons with shape changing for a generalized nonlinear Schrödinger equation in an optical fiber

Formation of solitons with shape changing for a generalized nonlinear Schrödinger equation in an optical fiber

Nozaki-Bekki solitons in semiconductor lasers.

Optical frequency-comb sources, which emit perfectly periodic and coherent waveforms of light1, have recently rapidly progressed towards chip-scale integrated solutions. Among them, two classes are particularly significant-semiconductor Fabry-Perót lasers2-6 and passive ring Kerr microresonators7-9. Here we merge the two technologies in a ring semiconductor laser10,11 and demonstrate a paradigm for the formation of free-running solitons, called Nozaki-Bekki solitons. These dissipative waveforms emerge in a family of travelling localized dark pulses, known within the complex Ginzburg-Landau equation12-14. We show that Nozaki-Bekki solitons are structurally stable in a ring laser and form spontaneously with tuning of the laser bias, eliminating the need for an external optical pump. By combining conclusive experimental findings and a complementary elaborate theoretical model, we reveal the salient characteristics of these solitons and provide guidelines for their generation. Beyond the fundamental soliton circulating inside the ring laser, we demonstrate multisoliton states as well, verifying their localized nature and offering an insight into formation of soliton crystals15. Our results consolidate a monolithic electrically driven platform for direct soliton generation and open the door for a research field at the junction of laser multimode dynamics and Kerr parametric processes.

Optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle.

In this paper, we investigate the optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle. We derive the nondegenerate bright one- and two-soliton solutions by solving the coupled Schrödinger equation. The formation of nondegenerate solitons is related to the wave numbers of the solitons, and we further demonstrate that it is caused by the incoherent addition of different components. We note that the interaction between two degenerate solitons or a nondegenerate soliton and a degenerate soliton is usually inelastic. This is led to the incoherent interaction between solitons of different components and the coherent interaction between solitons of the same component. Through the asymptotic analysis, we find that the two degenerate solitons are elastic interactions under certain conditions, and analyzed the influence of the Kerr nonlinear intensity coefficient γ and the second-order group velocity dispersion β2 in this system on solitons: the velocity and amplitude of the solitons are proportional to |β2|, while the amplitude of the solitons is inversely proportional to γ. Two nondegenerate solitons are elastic interactions, but the phase of the soliton can be adjusted to make it inelastic. Furthermore, regardless of the situation mentioned above, total intensities of the solitons before the interaction are equal to that after the soliton interaction.

Formation of solitons for the modified nonlinear Schrödinger equation

The study of modified nonlinear Schrödinger equation plays a significant role in the description of wave propagation through optical waveguides and rogue waves in ocean. The main aim of this work is to obtain solitons as well as other types of exact wave solutions to the modified nonlinear Schrödinger equation. The accurate traveling wave solutions are obtained using the [Formula: see text]-exponential expansion method and the modified auxiliary equation method. Consequently, soliton solutions and periodic wave solutions have been retrieved. The graphical illustrations of the results are provided for suitable values of the parameters involved in the solutions to explain the dynamical nature of the considered equation.

The Efficient Method to Solve the Conformable Time Fractional Benney Equation

The current study employed the innovative conformable fractional method to analyze the nonlinear Benney equations involving the conformable fractional derivative. Conformable fractional Benney equations have been examined by the conformable q‐Shehu analysis transform method. By including nonlinear factors, it offers a more precise depiction of wave propagation compared to linear models. Various natural phenomena, including ocean waves, plasma waves, and some forms of solitons, display nonlinear behavior that cannot be precisely explained by linear equations. The fractional Benney equation is important because it extends the classical Benney equation, which describes the evolution of weakly nonlinear and weakly dispersive long waves in shallow water. By incorporating fractional calculus operators, the fractional Benney equation provides a more accurate description of wave propagation phenomena in certain physical systems characterized by nonlocal or memory‐dependent behavior. The utilization of the Benney equation enables researchers to simulate these occurrences with greater realism. This study investigates the convergence and inaccuracy of the future scheme. The conformable q‐Shehu homotopy analysis transform method (Cq‐SHATM) generates h‐curves that demonstrate the convergence interval of the series solution obtained. In order to determine the effectiveness and suitability of the Cq‐SHATM, uniqueness and convergence theorems have been proven. This study presents an application that showcases the potential advantages and efficacy of the suggested method. Moreover, an error analysis is conducted to validate the precision of the scheme. Computational simulations are performed to verify the accuracy of the upcoming method. This study presents the results gained from the numerical and graphical analysis. The method presented in this work demonstrates a high level of computational accuracy and simplicity in analyzing and solving complex phenomena associated with conformable fractional nonlinear partial differential equations in the fields of science and technology.

Controlled pulse generation and annihilation dynamics in ultrafast fiber lasers

In this paper, the mode-locked pulse generation and annihilation dynamics in ultrafast fiber lasers based on pump intensity modulation are investigated by using real-time Fourier transform spectral probing. The results show that the laser outputs stable mode-locked pulses when the pump modulation voltage is at a high level. As the modulation voltage jumps to a low level, the intensity of the mode-locked pulse decreases, and then undergoes a period of decaying oscillation before annihilation occurs, and after ~5 μs the soliton is reconstructed from the noise, accompanied by the generation of the <i>Q</i>-modulation instability. In the low-level phase, the annihilation process in the laser cavity occurs continuously with a period of ~55 μs. By changing the duty cycle of the modulation pump, it is possible to control the the number of times solitons continuously annihilate under low-level modulation. Further, the continuous switching process of mode-locking and soliton annihilation is related to the modulation frequency of the pump, and the increase of the modulation frequency can effectively shorten the duration of the two states, thus reducing the number of soliton annihilations. In addition, by reducing the value of the low level, the gain in the laser cavity can be reduced, resulting in a shorter period of successive soliton annihilation. The results of the study are conducive to an in-depth understanding of the formation and annihilation dynamics of solitons, and provide new perspectives for developing various operation mechanisms of ultrafast lasers.

Storage and retrieval of optical solitons in nanofiber-semiconductor quantum dot molecule coupling systems

The best carrier for quantum information transmission is light signal, which has a fast propagation speed and can carry a large amount of information. However, during the propagation of light, dispersion effect and diffraction effect can cause quantum information to be distorted to a certain extent. On the contrary, optical solitons are formed due to the balance between the system’s dispersion (diffraction) effect and nonlinear effect, and they exhibit very high stability and fidelity. Therefore, they have received widespread attention in electromagnetically induced transparency (EIT) media with ultracold atoms. However, cold atomic gas media require extremely low operating temperatures, and the performances of the materials are difficult to control precisely. These factors are unfavorable for the miniaturization and integration of future information devices, thus significantly limiting their practical applications. Semiconductor quantum dot media, on the other hand, possess advantages such as discrete energy level structures and spectral properties similar to those of cold atomic gases, longer decoherence times, larger electric dipole moments, more significant nonlinear optical effects, and easy integration, making them an ideal alternative to cold atomic media. In this work, semiconductor quantum dots are coupled with optical fibers, the most common carrier in optical communication, to explore the formation, storage, and retrieval of temporal optical solitons in the coupled system. The results show that due to the tunneling-induced transparency effect between dots in semiconductor quantum dot molecules, light absorption in the system is greatly suppressed. At the same time, the transverse confinement of the nanofiber can enhance the interaction between light and the system, and the enhanced nonlinear response of the system can balance the dispersion effect, resulting in stable temporal optical solitons. Further research indicates that by turning on and off the inter-dot tunneling coupling, the high-efficiency and high-fidelity storage and retrieval of optical solitons can be realized in the system. These findings have certain guiding significance and potential application value for the processing all-optical information in solid quantum materials.

Wave dynamics for the new generalized (3+1)-D Painlevé-type nonlinear evolution equation using efficient techniques

<p>In this paper, diverse wave solutions for the newly introduced (3+1)-dimensional Painlevé-type evolution equation were derived using the improved generalized Riccati equation and generalized Kudryashov methods. This equation is now widely used in soliton theory, nonlinear wave theory, and plasma physics to study instabilities and the evolution of plasma waves. Using these methods, combined with wave transformation and homogeneous balancing techniques, we obtained concise and general wave solutions for the Painlevé-type equation. These solutions included rational exponential, trigonometric, and hyperbolic function solutions. Some of the obtained solutions for the Painlevé-type equation were plotted in terms of 3D, 2D, and contour graphs to depict the various exciting wave patterns that can occur. As the value of the amplitude increased in the investigated solutions, we observed the evolution of dark and bright solutions into rogue waves in the forms of Kuztnetsov-Ma breather and Peregrine-like solitons. Other exciting wave patterns observed in this work included the evolution of kink and multiple wave solitons at different time levels. We believe that the solutions obtained in this paper were concise and more general than existing ones and will be of great use in the study of solitons, nonlinear waves, and plasma physics.</p>

Optical fractals and Hump soliton structures in integrable Kuralay-Ⅱ system

<p>The integrable Kuralay-Ⅱ system (K-IIS) plays a significant role in discovering unique complex nonlinear wave phenomena that are particularly useful in optics. This system enhances our understanding of the intricate dynamics involved in wave interactions, solitons, and nonlinear effects in optical phenomena. Using the Riccati modified extended simple equation method (RMESEM), the primary objective of this research project was to analytically find and analyze a wide range of new soliton solutions, particularly fractal soliton solutions, in trigonometric, exponential, rational, hyperbolic, and rational-hyperbolic expressions for K-IIS. Some of these solutions displayed a combination of contour, two-dimensional, and three-dimensional visualizations. This clearly demonstrates that the generated solitons solutions are fractals due to the instability produced by periodic-axial perturbation in complex solutions. In contrast, the genuine solutions, within the framework of K-IIS, take the form of hump solitons. This work demonstrates the adaptability of the K-IIS for studying intricate nonlinear phenomena in a wide range of scientific and practical disciplines. The results of this work will eventually significantly influence our comprehension and analysis of nonlinear wave dynamics in related physical systems.</p>

The Study of Soliton Propagation in Optical Fibers

Abstract: In optical fibres, soliton formation results from a balance between the chirps produced by GVD and SPM, which, when functioning separately, both restrict the system's performance. We will analyse the dispersion-induced pulse broadening and the nonlinear optical effects to understand how such a balance is feasible. During an optical pulse's propagation inside an optical fibre, the GVD broadens it, unless the pulse is first chirped correctly. More precisely, whenever β2 and the chirp parameter C have opposing signs, resulting in β2C being negative, a chirped pulse is compressed at early phases of transmission. SPM causes the optical pulse to chirp so that C > 0. The criterion β2C < 0 can be easily met if β2 < 0. Furthermore, since the SPM-induced chirp is power-dependent, it is conceivable that, under some circumstances, SPM and GVD might work together to the point where the SPM-induced chirp is just the proper amount to cancel out the GVD-induced pulse broadening. In this case, an optical pulse propagates as a soliton with no distortion

The Stability and Behaviour of the Superposition of Non-Linear Waves in Space

The superposition of non-linear waves in space refers to the phenomenon where two or more waves overlap and combine to form a new wave pattern. Non-linear waves are characterized by their ability to interact with each other, leading to complex behaviors that are not observed in linear wave systems. Understanding the stability and behavior of the superposition of non-linear waves in space is crucial in various fields such as physics, engineering, and oceanography. When non-linear waves superpose, their interactions can lead to a range of behaviors, including wave breaking, formation of solitons (localized wave packets), and the generation of harmonics. The stability of the superposition is determined by the balance between the non-linear effects and dispersive effects, which can either stabilize or destabilize the wave pattern. In addition, the behavior of non-linear waves in space is influenced by external factors such as boundaries, dissipation, and external forcing. In this paper, we study the behavior and characteristics of waves when they interact with each other. Superposition refers to the phenomenon where multiple waves combine to form a resultant wave. In the case of linear waves, this superposition occurs according to the principles of linear superposition, which states that the displacement or amplitude at any point is the algebraic sum of the displacements or amplitudes of the individual waves. Understanding the superposition of linear waves in space has various applications in fields such as physics, engineering, acoustics, optics, and signal processing. By studying how waves interact and combine, researchers can gain insights into wave propagation, interference patterns, wave reflections, diffraction, and other phenomena that occur when waves meet.

Bicrystallography-informed Frenkel–Kontorova model for interlayer dislocations in strained 2D heterostructures

In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena originating from correlated electronic states harbored by them. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems, providing means of manipulation of these materials and allowing them to be tailored for emergent technologies. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene — a well-known heterostructure system that features moiré patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. In this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations. We anticipate that the model will be invaluable in predicting structural relaxation and for providing insights into various heterostructure systems, especially in cases where the fundamental unit cell is large and therefore, atomistic simulations are computationally expensive.

Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis

In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel techniques used to explore the solitary wave structures namely as; generalized Riccati equation mapping and modified auxiliary equation (MAE) methods. The different types of abundant families of solutions in the form of dark soliton, bright soliton, solitary wave solutions, mixed singular soliton, mixed dark-bright soliton, periodic wave, and mixed periodic solutions. The linearized stability of the model has been investigated. Solitons behave differently in different circumstances, and their behaviour can be better understood by building unique physical problems with particular boundary conditions (BCs) and starting conditions (ICs) based on accurate soliton solutions. So, the choice of unique physical problems from various solutions is also carried out. The 3D, line graphs and corresponding contours are drawn with the help of the Mathematica software that explains the physical behavior of the state variable. This information can help the researchers in their understanding of the physical conditions.

Universal gravitational waves from interacting and clustered solitons

Causal soliton formation (e.g. oscillons, Q-balls) in the primordial Universe is expected to give rise to a universal gravitational wave (GW) background, at frequencies smaller than scales of nonlinearity. We show that modifications of the soliton density field, driven by soliton interactions or initial conditions, can significantly enhance universal GWs. Gravitational clustering of solitons naturally leads to generation of correlations in the large-scale soliton density field. As we demonstrate for axion-like particle (ALP) oscillons, the growing power spectrum amplifies universal GW signals, opening new avenues for probing the physics of the early Universe with upcoming GW experiments. Our results are applicable to variety of scenarios, such as solitons interacting through a long range Yukawa-like fifth force.

Propagation characteristics of astigmatic elliptic vortex beams in nonlocal media with anisotropic nonlinearity

The propagation characteristics of the astigmatic elliptic vortex beam (AEVB) in nonlocal media with isotropic and anisotropic nonlinearities are analytically and numerically investigated. Three different kinds of dynamics are discussed: AEVB in nonlinear isotropic media, elliptic vortex beam in nonlinear anisotropic media, and astigmatic circular vortex beam (ACVB) in nonlinear anisotropic media. The isotropic nonlinearity cannot support the formation of elliptic vortex solitons for any input power, and the initial phase-front curvature (IPC) will induce the pulsating behavior of the AEVB. For anisotropic nonlinearity, when the nonlinear anisotropic parameter (NAP) of the medium and the initial ratio of the beam width satisfy γx/γy = (w0y/w0x)2, a quasi-stable elliptic vortex soliton can be obtained, in which the vortex angular velocity and vortex rotation angle evolve periodically. Circular vortex soliton cannot exist in nonlinear anisotropic media, and the rotation of the ACVB can be controlled by adjusting the NAP and the IPC. In both isotropic and anisotropic nonlinear media, the rotation direction of the vortex core is opposite to that of the beam envelope.