- 标题
- 摘要
- 关键词
- 实验方案
- 产品
-
Combined multi-waves rational solutions for complex Ginzburg–Landau equation with Kerr law of nonlinearity
摘要： By utilizing the logarithmic transformation and symbolic computation with ansatz functions technique, rational solution and multi-waves interaction solutions are obtained for complex Ginzburg–Landau equation with Kerr law of nonlinearity. Meanwhile, the interaction between rational solutions and the kink wave is also investigated. The dynamics of these obtained solutions are analyzed and described in figures by selecting appropriate values of parameters. Through graphical interpretation, we observe the dynamics and characteristics of lump-kink interaction, soliton–soliton interaction, multi-waves interactions and breathers.
关键词： complex Ginzburg–Landau equation.,logarithmic transformations,multi-waves interactions,Rational solutions
更新于2025-09-23 15:22:29
-
Stable soliton propagation in a coupled (2+1) dimensional Ginzburg-Landau system
摘要： In this paper, a coupled (2+1)-dimensional variable coefficient Ginzburg-Landau equation is studied. By virtue of the modified Hirota bilinear method, the bright one-soliton solution of the equation is derived. Some phenomena of soliton propagation are analyzed by setting different values of the dispersion term. The influences of the corresponding parameters on solitons are also discussed. Results can enrich the soliton theory, and may be helpful in the manufacture of optical devices.
关键词： modified Hirota bilinear method,Ginzburg-Landau equation,Soliton,bright soliton solution
更新于2025-09-23 15:21:01
-
Mutual transitions between stationary and moving dissipative solitons
摘要： Application of stable localized dissipative solitons as basic carriers of information promises the significant progress in the development of new optical communication networks. The success development of such systems requires getting the full control over soliton waveforms. In this paper we use the fundamental model of dissipative solitons in the form of the complex Ginzburg-Landau equation with a potential term to demonstrate controllable transitions between different types of coexisted waveforms of stationary and moving dissipative solitons. Namely, we consider mutual transitions between so-called plain (fundamental soliton), composite, and moving pulses. We found necessary features of transverse spatial distributions of locally applied (along the propagation distance) attractive potentials to perform those waveform transitions. We revealed that a one-peaked symmetric potential transits the input pulses to the plain pulse, while a two-peaked symmetric (asymmetric) potential performs the transitions of the input pulses to the composite (moving) pulse.
关键词： Control potential,Dissipative solitons,Waveform transitions,Complex Ginzburg-Landau equation
更新于2025-09-19 17:15:36
-
Soliton Behaviours for the Conformable Spacea??Time Fractional Complex Ginzburga??Landau Equation in Optical Fibers
摘要： In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a ?rst-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.
关键词： optical solitons,Weierstrass elliptic function,Ginzburg–Landau equation
更新于2025-09-16 10:30:52
-
Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals || Self-Organization, Coherence and Turbulence in Laser Optics
摘要： In the last decades, rapid progress in modern nonlinear science was marked by the development of the concept of dissipative soliton (DS). This concept is highly useful in many different fields of science ranging from field theory, optics, and condensed matter physics to biology, medicine, and even sociology. This chapter aims to present a DS appearance from random fluctuations, development and growth, the formation of the nontrivial internal structure of mature DS and its breakup, in other words, a full life cycle of DS as a self-organized object. Our extensive numerical simulations of the generalized cubic-quintic nonlinear Ginzburg-Landau equation, which models, in particular, dynamics of mode-locked fiber lasers, demonstrate a close analogy between the properties of DS and the general properties of turbulent and chaotic systems. In particular, we show a disintegration of DS into a noncoherent (or partially coherent) multisoliton complex. Thus, a DS can be interpreted as a complex of nonlinearly coupled coherent “internal modes” that allows developing the kinetic and thermodynamic theory of the nonequilibrious dissipative phenomena. Also, we demonstrate an improvement of DS integrity and, as a result, its disintegration suppression due to noninstantaneous nonlinearity caused by the stimulated Raman scattering. This effect leads to an appearance of a new coherent structure, namely, a dissipative Raman soliton.
关键词： dissipative solitons,chaos in nonlinear optical systems,generalized cubic-quintic nonlinear Ginzburg-Landau equation,dissipative Raman soliton,optical turbulence
更新于2025-09-12 10:27:22
-
Optical Solitons With M-Truncated and Beta Derivatives in Nonlinear Optics
摘要： This paper studies optical solitons with M-truncated and beta derivatives (BD) for the Complex Ginzburg-Landau equation (CGLE) with Kerr Law nonlinearity. Two well-known integration schemes which are generalized tanh method (GTM) and generalized Bernoulli sub-ODE method (GBM) are utilized to extract such optical soliton solutions. For the successful existence of the solutions, the constraints conditions have been presented. The discussion for the physical features of the obtained solutions is reported.
关键词： complex Ginzburg-Landau equation,optical solitons,generalized Bernoulli sub-ODE method,generalized tanh method,beta derivative
更新于2025-09-11 14:15:04
-
[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems
摘要： The conventional Fourier transform is widely used mathematical methods in science and technology. It allows representing the signal/field under study as a set of spectral harmonics, that it many situations simplify understanding of such signal/field. In some linear equations, where spectral harmonics evolve independently of each other, the Fourier transform provides a straightforward description of otherwise complex dynamics. Something similar is available for certain classes of nonlinear equations that are integrable using the inverse scattering transform [1, 2], also known as the nonlinear Fourier transform (NFT). Here we discuss potential of its application in dissipative, non-integrable systems to characterize coherent structures. We present a new approach for describing the evolution of a nonlinear system considering the cubic Ginzburg-Landau Equation (CGLE) as a particularly important example in the context of laser system modeling.
关键词： Coherent Structures,Ginzburg-Landau Equation,Dissipative Systems,Nonlinear Fourier Transform
更新于2025-09-11 14:15:04
-
Super Gaussian pulse generation in a passively mode-locked fiber laser
摘要： The generation of self-similar super Gaussian-like pulses from a passively mode-locked fiber laser is numerically demonstrated. The laser cavity utilizes a long period fiber grating as a pulse-shaping element. The model is based on the normalized complex Ginzburg-Landau equation and the nonlinear coupled mode equations of the grating. The numerical results show stable super Gaussian pulses with a linear frequency chirp, a 1.5 ps pulse duration and 2 nJ energy. The generated pulses are scalable and exhibits no bifurcation or instability as the gain is increased.
关键词： Mode-locked fiber lasers,Ginzburg-Landau equation,Kerr nonlinearity,Self-similar pulses,Numerical methods
更新于2025-09-11 14:15:04