Interaction Of Solitons Research Articles

Interaction of solitons in nonlocal media under competing nonlinearities with gradual nonlocality

We have numerically studied the interaction of in-phase and out-of-phase bright solitons in nematic liquid crystals with competing nonlinearities. In particular, we propose the nonlocality management technique to steer the beam interaction in nematic liquid crystals with competing nonlinearities. By controlling the degree of nonlocality of the material, three methods of regulating the degree of nonlocality were proposed to control soliton interactions. It was found that out-of-phase soliton pairs exhibit approximately adiabatic propagation under cosine function type regression control. To our knowledge, this is the first observation of adiabatic propagation of out-of-phase soliton pairs in nonlocal media with competing nonlinearities. Controlling soliton interactions by regulating the degree of nonlocality may provide theoretical guidance for the experimental realization of all-optical interconnections and all-optical devices.

Three-component soliton states in spinor F = 1 Bose-Einstein condensates with PT-symmetric generalized Scarf-II potentials

Abstract Introducing PT-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seeking stable soliton states in quasi-one-dimensional spin-1 Bose-Einstein condensates. In scenarios where the spin-independent parameter c_0 and the spin-dependent parameter c_2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c_2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.

Resonant soliton interaction for the Date–Jimbo–Kashiwara–Miwa equation

Investigated in this paper is the resonant soliton interactions for the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. A comprehensive classification of these interactions is presented, based on the exact expression of resonant soliton branches derived from asymptotic analysis. Two types of resonant interactions between two solitons are identified, characterized by the parameter Aij, which directly determines the phase shift. One-resonant and two-resonant three-soliton interactions are discussed, in which certain new soliton branches are revealed. Some graphical analyses are provided to illustrate these resonant interactions.

Study of Fifth-Order Nonlinear Caudrey–Dodd–Gibbon Model for Multiwave, M-Shaped Solitons, Lumps, Generalized Breathers, Manifold Periodic, Rogue Wave and Kink Wave Interactions

Numerous novel wave structures, such as lump, lump with one-kink, lump with two-kink soliton, generalized breather, Ma breather, Kuznetsov-Ma breather, Akhmediev breather, manifold periodic, and rogue wave solutions to [Formula: see text]-dimensional fifth-order nonlinear Caudrey–Dodd–Gibbon (FNCDG) model via symbolic computation are studied based on the ansatz function scheme. Studying the lump-type solution involves selecting the function as the generic quadratic polynomial function. The lump with one- and two-kink solutions is created by mixing a quadratic function with one or two exponential functions. By adding hyperbolic function with a quadratic function, the rogue wave solutions are manipulated. In addition, the multiwave, [Formula: see text]-shaped rational solitons and their interactions with kink waves are analytically evaluated. Furthermore, different 3D, 2D, and contour profiles are created in different dimensions by changing the parameter values.

On the study of analytical soliton solutions and interaction aspects to the Estevez-Mansfield-Clarkson equation arising in diversity of fields

Abstract The beta fractional form of the Estevez-Mansfield-Clarkson equation is under consideration and this study is done with the assistance of methods such as modified F-expansion method and the logarithmic transformation. A variety of analytical solutions like bright, dark, mixed, singular, bright-dark, and combined solitons are extracted. Moreover, multi waves structures, interaction with double exponential form, breather waves, mixed type solutions as well as periodic cross kink solutions have been analyzed. The governing equation is converted into an ordinary differential equation by employing an appropriate wave transformation with the β-derivative in order to achieve the desired solutions. The applied approaches have substantial computational capability, enabling them to efficiently address exact solutions with high accuracy in these systems. The results indicate that the equation under investigation theoretically contains a substantial number of soliton solution structures. Additionally, in order to examine the behaviors of the solutions at various parameter values, we plot a variety of graphs that incorporate pertinent parameters. The results of this study have the potential to improve understanding of the nonlinear dynamic characteristics displayed by the specified system and to confirm the effectiveness of the techniques that have been implemented.

Observation of widely separated soliton molecules in a mode-locked Yb-doped fiber laser operating with net anomalous dispersion

This paper investigates the generation and characterization of soliton molecules (SM) in a semiconductor saturable absorber mirror (SESAM) mode-locked Yb-doped fiber laser with a linear cavity. By adjusting the pump power, both single-pulsing (SP) and double-pulsing (DP) states can be achieved. The observed soliton molecules are highly stable, with minimal temporal jitter despite being separated by 1.56ns. While SM have been observed in many different cavities this is one of the few reports in a Fabry–Perot cavity rather than a ring cavity and again most previous observations of soliton molecules having been in the anomalous dispersion regime. This configuration thus provides detailed and valuable insights into the behaviour of SM, shedding light on their formation, stability, and dynamics. This study contributes to understanding long range soliton interactions in fiber lasers, with potential implications for applications such as multi-bit transmission, bit storage, and pump-probe experiments to study the dynamics of chemical reactions.

Breathers, Lump, M-shapes and Other Optical Soliton Interactions for the GRIN Multimode Optical Fiber

Breathers, Lump, M-shapes and Other Optical Soliton Interactions for the GRIN Multimode Optical Fiber

Analysis of optical soliton interactions and their parallel transmission characteristics in optical fibers

Analysis of optical soliton interactions and their parallel transmission characteristics in optical fibers

Features of Radio Emission Propagation in the Ionosphere under Conditions of Threshold Nonlinearity

The well-known problem of nonlinear “wave – ionosphere” interaction under conditions of threshold nonlinearity is considered. It is believed that nonlinear effects arise only for high-power radiation, when the wave amplitude exceeds a certain threshold value. The possibility of the existence of concentrated wave fields under these conditions is shown. It is revealed that a certain ratio of nonlinearity parameters leads to an increase in the radio emission intensity, since the interaction of individual solitons can lead to their merging into a higher-power solitary wave. The presence of threshold nonlinearity can lead to the formation of an ordered structure of solitary waves.

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

The theoretical study of high-order dissipation soliton molecules evolution in a passively mode-locked fiber laser

High-order solitons represent a special form of soliton. Due to the complexity of their spatial structure and dynamic evolution, they have important applications in communication systems such as wavelength division multiplexing and secure communication. However, compared to traditional solitons, research on the spectral evolution of high-order solitons is still insufficient. In this paper, through precise control of laser parameters, the dynamic evolution process from stable dissipative single soliton to complex dissipative 8-order soliton molecules in passively mode-locked fiber lasers was successfully simulated. This demonstrates the complexity of solitons interaction and reveals the regularity of soliton molecules order with variations in four parameters: the small signal gain coefficient, nonlinear coefficient, gain bandwidth and the polarization controller angle. Through deep analysis of the order of soliton molecules, pulse shape and spectral shape of dissipative soliton molecules, we showcase the potential of fine-tuning laser parameters to achieve high-order dissipative soliton molecules. This work provides important references for the optimization design and expanded applications of lasers, further driving the development of high-performance, high-efficiency fiber laser technology.

Interaction of Solitons with Inhomogeneous Defects in Nonlocal Nonlinear Media

Interaction of Solitons with Inhomogeneous Defects in Nonlocal Nonlinear Media

Energy-conserving SAV-Hermite–Galerkin spectral scheme with time adaptive method for coupled nonlinear Klein–Gordon system in multi-dimensional unbounded domains

In this article, we construct an efficient numerical scheme to solve the coupled nonlinear Klein–Gordon system in a multi-dimensional unbounded domain Rd(d=1,2,3). We first use the SAV method to equivalently deform the original system, then we treat the nonlinear part of the system explicitly in temporal discretization. Thanks to the SAV method, we ensure the unconditional energy conservation of the discrete system, as a cost, we only need to solve two completely linearized decoupled systems. To avoid the errors caused by domain truncation and the construction of artificial boundary conditions, we apply the Hermite–Galerkin spectral method with scaling factor for spatial discretization. In order to save computational costs, we utilize two time adaptive strategies to adjust the time step size, through which we can improve computational efficiency without sacrificing accuracy. Finally, we presented numerical experiments to demonstrate the accuracy, efficiency, and energy conservation properties of our algorithm, and applied it to simulate the interactions of two-dimensional and three-dimensional vector solitons.

Dynamics of geometric shape solutions for space-time fractional modified equal width equation with beta derivative

The modified equal width equation describes the propagation of shallow water waves in which nonlinear and dispersive effects are significant, including phenomena such as wave breaking, soliton interactions, ion-acoustic waves, energy transfer in plasma, and nonlinear stress waves. The aim of this article is to establish some novel and generic solutions to the space-time fractional modified equal width (MEW) equation using the two variable (θ′/θ, 1/θ)-expansion technique, a modification of the (θ′/θ)-expansion method. A wide range of geometric shapes and inclusive soliton solutions have been constructed, comprising rational, trigonometric, and hyperbolic solutions, along with their integration to the equation under consideration. The two- and three-dimensional graphs of the solitons, including periodic, V-shaped, bell-shaped, singular periodic, flat kink-shaped, plane-shaped, peakon, and parabolic, illustrate the physical aspects of the solitary wave solution and the effect of the fractional parameter. The results demonstrate the efficiency, appropriateness, and reliability of the adopted technique for investigating fractional-order nonlinear evolution equations in science, technology, and engineering.

Interaction of solitons in the matrix nonlinear Schrödinger equation

In this paper, we study a matrix nonlinear Schrödinger (MNLS) equation with high-order effects. Through the Darboux transformation, we construct soliton solutions of the MNLS equation up to the second order. Based on the analytic solutions, proper parameters are chosen to display evolution and elastic interaction of the solitons.

Coherence-controlled chaotic soliton bunch

Controlling the coherence of chaotic soliton bunch holds the promise to explore novel light-matter interactions and manipulate dynamic events such as rogue waves. However, the coherence control of chaotic soliton bunch remains challenging, as there is a lack of dynamic equilibrium mechanism for stochastic soliton interactions. Here, we develop a strategy to effectively control the coherence of chaotic soliton bunch in a laser. We show that by introducing a lumped fourth-order-dispersion (FOD), the soliton oscillating tails can be formed and generate the potential barriers among the chaotic solitons. The repulsive force between neighboring solitons enabled by the potential barriers gives rise to an alleviation of the soliton fusion/annihilation from stochastic interactions, endowing the capability to control the coherence in chaotic soliton bunch. We envision that this result provides a promising test-bed for a variety of dynamical complexity science and brings new insights into the nonlinear behavior of chaotic laser sources.

Nonlinear-Optical Analogies in Nuclear-Like Soliton Reactions: Selection Rules, Nonlinear Tunneling and Sub-Barrier Fusion–Fission

Abstract The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics, which still remain hidden from us. We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons. On the base of this model, we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton self-induced sub-barrier transparency effect. We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions. The main finding of this study concerns the conservation of total number of nucleons (or the baryon number) in nuclear-like soliton reactions. We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a “cloud” of “dressing” spectral side-bands appears in the frequency spectra of the solitons. This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter. Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors. We show that the nuclear-like reactions between well-dressed solitons are realized by “exchange” between “particle-like” side bands in their spectra.

Diffraction and Interaction of Interfacial Solitons in a Two-Layer Fluid of Great Depth

Diffraction and Interaction of Interfacial Solitons in a Two-Layer Fluid of Great Depth

Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions

Abstract When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schrödinger equation, we analytically explore the evolution of optical solitons in the presence of high-order nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.

A Poisson-bracket scheme for nonlinear shallow-water sloshing in an oscillating tank with irregular bottom surface

The mass-, energy-, and potential-enstrophy-conserving Poisson bracket numerical scheme introduced by Arakawa & Lamb (1981), and extended by Salmon (2004) and Stewart & Dellar (2016), is adapted to the problem of nonlinear shallow-water sloshing over a variable bottom surface in a rigid rectangular basin undergoing a prescribed coupled surge-sway motion. Adaptation to a finite domain requires a new approach to the boundary conditions at solid boundaries in the context of the Arakawa C grid. In this paper, the boundary condition at the vertical walls is taken to be vanishing of the normal derivative of the tangential velocity. This gives zero potential vorticity at the boundary, and is consistent with the material conservation of the potential vorticity. This condition, coupled to symmetric boundary conditions for the wave height arising from a reduced version of the evolution equations at boundaries, leads to an extension of the class of staggered C-grid Poisson-bracket schemes to interior flows with solid boundaries. The scheme is implemented, shown to preserve Casimirs, and applied to a range of problems in shallow water hydrodynamics including interaction of travelling hydraulic jumps at resonance, and X-type soliton interactions over a variable bottom surface. This structure-preserving scheme provides a robust building block for long-time simulation of floating ocean wave energy extractors.