Dark Breathers Research Articles

Dark Soliton and Breather Solutions to the Coupled Sasa–Satsuma Equation

Dark Soliton and Breather Solutions to the Coupled Sasa–Satsuma Equation

Dark breathers on a snoidal wave background in the defocusing mKdV equation

Dark breathers on a snoidal wave background in the defocusing mKdV equation

Exploration of soliton structures in the Hirota–Maccari system with stability analysis

In this research, the modified extended tanh-function (METF) and the extended Jacobi elliptic function expansion (EJEFE) techniques are used to investigate the generation and detection of soliton structures in the Hirota–Maccari (HM) model. Consequently, we obtain soliton solutions with advanced structures, including singular bright soliton, dark soliton, periodic waves, breather waves, periodic breather waves, and multiple bright and dark breather waves. In addition, a lump-type breather wave is also included in the presented solutions. Stability analysis of the obtained solutions is addressed by employing the Hamiltonian technique. 3D surfaces and 2D visuals of the outcomes are represented with the help of a computer application. These findings contribute to understanding nonlinear wave phenomena with potential applications in optics, fluid dynamics, and plasma physics.

Soliton dynamics and multistability analysis of the Hamiltonian amplitude model

This work delivers the soliton outcomes through the 1G′ scheme, the modified extended tanh-function (METF) method, and the 1G,G′G approach to the Hamiltonian amplitude (HA) model. The multiple bright dark breather waves with singular solution, bright dark breather waves with singularity, periodic waves, double periodic waves, dark soliton, and bright soliton are formed from this system with the help of the above three techniques via computer software. 2D phase portraits and Poincaré plots study the multistability of the mentioned model. Furthermore, a comparison is shown between this research and some recently published work to check the uniqueness of this research. In addition, 3D curves with density plots and 2D diagrams represent the behavior of solitons. The conclusions of this study have implications for further research in this field. The study also provides a better understanding of the behavior of solitons.

Fragmentation of stability domains of dark solitons, dark breathers, and drifting solitons at high pump intensities in normal-dispersion Kerr microresonators

Fragmentation of stability domains of dark solitons, dark breathers, and drifting solitons at high pump intensities in normal-dispersion Kerr microresonators

Magnetic soliton and breather interactions for the higher-order Heisenberg ferromagnetic equation via the iterative N-fold Darboux transformation

This paper focuses on a higher-order Heisenberg ferromagnetic equation, which may describe the motion of the magnetic vector of isotropic ferromagnetism. The iterative N-fold Darboux transformation is first constructed to generate the dark and anti-dark magnetic solitons on the non-zero constant backgrounds, bright and dark breathers on the trigonometric function and non-zero constant backgrounds as well as breathers on the trigonometric function and vanishing backgrounds. We discover that the soliton structures of three different components can generate rotation with different constant seed solutions. Meanwhile, the trajectory curve and the direction of the magnetic vector are also discussed from the perspective of magnetism, we find that for constant seed solutions, the motion of the magnetic vector is limited to the hemisphere, while for trigonometric seed solutions, the motion of the magnetic vector can be distributed throughout the whole sphere. These novel phenomena may be helpful to understand the dynamics of the magnetic vector in the magnetic materials.

Families of exact solutions of a Generalized (2+1)-dimensional Boussinesq type equation

In this paper, we study a Generalized (2+1)-dimensional Boussinesq-type equation. Using the Hirota bilinear method, we present the N-order bright soliton solutions and dark soliton solutions. For the one-soliton solution, the bright soliton solution and the dark soliton solution share the same limit line but have different extreme values. Building on the soliton solutions, we derive higher-order bright and dark breather solutions as well as mixed solutions. The dynamic behavior is characterized using visual representations. Furthermore, through the long-wave limit method, we obtain the bright and dark lump solutions. Notably, they share the same extreme points but have different extreme values. Additionally, we derive two semi-rational solutions as lump-soliton and lump-breather. It is found that the lump moves along the peak amplitude of the soliton wave.

Bright and dark breathers of the Benjamin–Ono equation on the traveling periodic background

The Benjamin–Ono (BO) equation describes long internal waves of small amplitude in deep fluids. Compared to its counterpart for shallow fluids, the Korteweg–de Vries (KdV) equation, the BO equation admits exact solutions for the traveling periodic and solitary waves as well as their interactions expressed in elementary (trigonometric and polynomial) functions. Motivated by a recent progress for the KdV equation, we discover here two scenarios of the soliton-periodic wave interactions which result in the propagation of either elevation (bright) or depression (dark) breathers (periodic in time coherent structures). The existence of two different breathers is related to the band-gap spectrum of the Lax operator associated with the traveling periodic wave. Given a simple structure of the exact solutions in the BO equation, we obtain a closed-form expression for multi-solitons interacting with the traveling periodic wave.

Interaction solution to the (3+1)-D negative-order KdV first structure

We derive N-solitons and interaction solution for the (3+1)-D negative-order KdV first structure that arises in shallow-water waves. We use the bilinear scheme and the simplified Hirota technique for this solution. From the multiple solitons solution, we obtain a lump-shaped breather wave, a lump-shaped breather with a kink wave, and two lump-shaped breather waves from 2-solitons, 3-solitons, and 4-solitons, sequentially, by choosing complex conjugates of related parametric constants. Additionally, we show some novel interactions of the Jacobian elliptic transformation with periodic function, single soliton, and two solitons. Owing to these collisions, periodic waves with a kink wave, periodic breathers with a kink wave, and numerous bright and dark breather waves are created. We illustrate the properties of these solutions with 3D, density, and contour plots by selecting the appropriate values for the parameters. The obtained solutions will serve as milestones for studying the properties of nonlinear structures in the physical sciences and engineering fields.

Nonlinear wave excitations in the (2+1)-D asymmetric Nizhnik-Novikov-Veselov system

The (2+1)-dimensional nonlinear asymmetric Nizhnik-Novikov-Veselov system is one of the extended versions of the Korteweg-de Vries equation, and as such of considerable significance in nonlinear wave dynamics. In this work, it is transformed into a bilinear form by using the Hirota transformation and then treated by the variable separation method. In particular, by separating variables in a specific manner, a class of solutions is obtained, which are constructed with the help of three auxiliary functions, Py, Ry, and Qxt. By selecting the three functions conveniently, we obtain novel nonlinear excitations for the asymmetric Nizhnik-Novikov-Veselov system. To make our results more explicit and interesting, various types of nonlinear profiles were displayed, colloquially named as the parallelogram, walnut, dark breather, half-moon breather, and the top-compressed quadrilateral breather structures. It is found that these local wave packets can be well controlled by appropriately selecting the three auxiliary functions, and that the variable separation approach can be extended to other high-dimensional nonlinear systems.

Influence of NNN interaction and existence of breathers in a quasi-discrete Heisenberg helimagnetic spin system

In this work, we investigate the existence and properties of discrete bright and dark breathers in a one-dimensional Heisenberg helimagnet incorporating bilinear, helical, NNN and anisotropic interactions. The Hamiltonian is bosonized using the Dyson–Maleev transformation and the coherent state representation is selected as the fundamental representation of the system. With the help of multiple scales combined with quasi-discreteness approximation, the dynamical equation is reduced to a nonlinear Schrödinger equation (NLSE). By employing the solution of NLSE derived using inverse scattering technique (IST), the bright and dark type breather solutions are constructed. The effect of helicity and NNN interactions on these breather modes is also analysed.

The nonlocal coupled nonlinear Schrödinger system with 𝒫𝒯-symmetric: Analytical solutions under two types of Darboux transformation

The coupled nonlinear Schrödinger (CNLS) system is often used to describe physical problems such as wave propagation in a birefringent optical fiber. Under investigation in this paper is the nonlocal [Formula: see text]-symmetric reverse-space type of CNLS system, through constructing two types of Darboux transformation (DT), we will derive a new series of nonlocal analytic solutions: (1) Single-periodic and double-periodic solutions; (2) Four different combinations about dark and anti-dark solitons, as well as the bright and dark breathers on a periodic background. Moreover, the fundamental properties and dynamical behaviors of those solutions will be discussed.

Soliton solutions for the Zoomeron model applying three analytical techniques.

The Zoomeron equation is used in various categories of soliton with unique characteristics that arise in different physical phenomena, such as fluid dynamics, laser physics, and nonlinear optics. To achieve soliton solutions for the Zoomeron nonlinear structure, we apply the unified, the Kudryashov, and the improved Kudryashov techniques. We find periodic, breather, kink, anti-kink, and dark-bell soliton solutions from the derived optical soliton solutions. Bright, dark, and bright-dark breather waves are also established. Finally, some dynamic properties of the acquired findings are displayed in 3D, density, and 2D views.

Novel dynamics of the Zoomeron model via different analytical methods

We apply the novel Kudryashov scheme, the 1G′ approach, and the G′G′+G+A technique to handle the Zoomeron model for the first time, which yields several kinds of soliton solutions with some novel dynamic properties. The proposed model handles specific incidents of soliton structures with distinctive characteristics that arise in laser sciences, fluid mechanics, and nonlinear optics. We observe dark soliton, bright soliton, periodic waves, kink waves, anti-kink waves, and breather waves for the mentioned equation by symbolic calculation. The suggested model also produces lump-type breather waves. Density, 3D, and 2D images are used to exhibit the dynamics of the adopted outcomes. The results will be crucial for future research on higher-order nonlinear models.

KdV breathers on a cnoidal wave background

Using the Darboux transformation for the Korteweg–de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character, these wave patterns are referred to as breathers. Both elevation (bright) and depression (dark) breather solutions are obtained. The nonlinear dispersion relations demonstrate that the bright (dark) breathers propagate faster (slower) than the background cnoidal wave. Two-soliton solutions are obtained in the limit of degeneration of the cnoidal wave. In the small amplitude regime, the dark breathers are accurately approximated by dark soliton solutions of the nonlinear Schrödinger equation. These results provide insight into recent experiments on soliton-dispersive shock wave interactions and soliton gases.

Stimulated Raman scattering induced dark pulse and microcomb generation in the mid-infrared

We demonstrate that strong stimulated Raman scattering in silicon and germanium microresonators can induce stable and breathing dark pulses generation circumventing traditional complex approaches such as pump modulation and mode coupling. Although multi-photon absorption shows a small influence on the detuning value for stable dark pulse excitation, the concomitant free carrier will assist dark pulse excitation and broaden the excitation area of dark pulse thus making it easier to capture stable pulse. Furthermore, dark breather dynamics in Si and Ge are also observed, which shows distinct properties from the dark soliton breathers dominated solely by Kerr effect. Finally, we show that octave spanning mid-infrared (MIR) microcomb can be generated combining with high-order dispersion engineering, which in turn affects the breathing dynamics of dark pulses. Our findings provide another way for the initiation of dark pulses in group IV materials and broadband MIR microcomb generation for spectroscopy applications.

The nth-Darboux Transformation and Explicit Solutions of the PT-Symmetry Second-Type Derivative Nonlinear Schrödinger Equation

Non-local problems have become one of the research hotspots in recent years since Ablowitz–Musslimani constructed an integrable non-local nonlinear hbox {Schr}ddot{mathrm{o}}hbox {dinger} (NLS) equation in 2013. In this paper, we first derive the PT-symmetry second derivative nonlinear hbox {Schr}ddot{mathrm{o}}hbox {dinger} (PT-DNLSII) equation. Then we present the nth-Darboux transformation (DT) of the PT-DNLSII equation. As applications, starting from the zero seed solution and non-zero periodic seed solution, the explicit expressions of the multi-soliton solutions, bright soliton solution, dark soliton solution and breather soliton solution of the PT-DNLSII equation are worked out.

Dark soliton solutions of the cubic-quintic complex Ginzburg–Landau equation with high-order terms and potential barriers in normal-dispersion fiber lasers

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained.

Dark discrete breather modes in a monoaxial chiral helimagnet with easy-plane anisotropy

Nonlinearity and discreteness are two pivotal factors for an emergence of discrete breather excitations in various media. We argue that these requirements are met in the forced ferromagnetic phase of the monoaxial chiral helimagnet $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$ due to the specific domain structure of the compound. The stationary, time-periodic breather modes appear as the discrete breather lattice solutions whose period mismatches with a system size. Thanks to easy-plane single-ion anisotropy intrinsic to $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$, these modes are of the dark type with frequencies lying within the linear spin-wave band, close to its bottom edge. They represent cnoidal states of magnetization, similar to the well-known soliton lattice ground state, with differing but limited number of embedded $2\ensuremath{\pi}$ kinks. The linear stability of these dark breather modes is verified by means of Floquet analysis. Their energy, which is controlled by two parameters, namely, the breather lattice period and amplitude, falls off linearly with a growth of the kink number. These results may pave a path to design spintronic resonators on the base of chiral helimagnets.

Breathers, interactions between breathers and lumps for a (3 + 1)-dimensional nonlinear evolution equation for the shallow-water waves

In the present paper, we investigate a -dimensional nonlinear evolution equation, which can be used to describe the shallow-water waves. Via the Kadomtsev–Petviashvili hierarchy reduction, we derive the breather, semi-rational and rational solutions in terms of Gramian. The breathers are dark breathers. Taking the long wave limit in the breather solutions, we derive the semi-rational solutions describing the interactions between the lumps and breathers, and the rational solutions which give birth to the lumps are also derived. Interactions between the lumps and breathers are elastic. Furthermore, we graphically present the interactions among the dark lumps. We find that the interactions among the three lumps are elastic.