- 标题
- 摘要
- 关键词
- 实验方案
- 产品
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Modulation stability analysis and solitary wave solutions of nonlinear higher-order Schr?dinger dynamical equation with second-order spatiotemporal dispersion
摘要： In optical fibers, the higher-order nonlinear Schr?dinger (NLS) dynamical equation which describes the beyond the classic slowly varying envelopes and spatiotemporal dispersion of pulses is investigated. By applying the proposed modified extended mapping method, the optical soliton solutions of higher-order NLS dynamical equation with the coefficients of group velocity dispersion, second-order spatiotemporal dispersion and cubic nonlinearity are deduced. The obtained solutions have important applications in applied sciences and engineering. The formation conditions are specified on parameters in which optical solitons can exist for this media. The moments of some constructed solutions are presented graphically which facilitate the researchers to comprehend the physical phenomena of this equation. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are stable and exact. Other such forms of the system arising in sciences and engineering can also be solved by this steadfast, influential and effective method.
关键词： Solitary wave solutions,Higher-order nonlinear Schr?dinger equation,Solitons,Modified extended mapping method
更新于2025-09-23 15:23:52
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Solitons solutions of nonlinear Schr?dinger equation in the left-handed metamaterials by three different technique
摘要： This paper, derives the exact traveling-wave solution and soliton solutions of nonlinear Schr?dinger equation (NLSE) with higher-order nonlinear terms of Left-handed metamaterials (LHMs), the authors apply three different methods, namely: csch function method, the exp(?φ(ξ))-Expansion method and the simplest equation method. The results obtained are Dark, Bright solitons and other solutions, which are well known in optics metamaterials and LHMs.
关键词： Exact Soliton solutions and other solutions of nonlinear Schr?dinger equation with higher-order nonlinear terms,the exp(?φ(ξ))-Expansion method method,csch function method,the simplest equation
更新于2025-09-23 15:22:29
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Relay-Zone Technique for Numerical Boundary Treatments in Simulating Dark Solitons
摘要： To simulate dark solitons in the defocusing nonlinear Schr?dinger equation, we introduce a relay-zone technique, by alternately using a Robin boundary condition to treat the nonzero far field, and a derivative boundary condition to match the dark soliton. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment. Stability and interaction of dark solitons are also studied.
关键词： Nonlinear Schr?dinger equation,Artificial boundary condition,Dark soliton
更新于2025-09-23 15:22:29
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Modulational instability and homoclinic orbit solutions in vector nonlinear Schr?dinger equation
摘要： Modulational instability has been used to explain the formation of breathers and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. In the first place, we develop a method to derive general forms for Akhmediev breathers, rogue waves and their multiple or high order ones in a N-component nonlinear Schr?dinger equations. The existence condition for each pattern is clarified clearly with a compact algebraic equation. Moreover, we show that the existence condition of ABs and RWs is consistent with the dispersion relation of the linear stability analysis on the background solution. The results further deepen our understanding on the quantitative relations between modulational instability and homoclinic orbits solutions.
关键词： general multi-high-order rogue wave,vector nonlinear Schr?dinger equation,modulational instability analysis,Akhmediev breathers
更新于2025-09-23 15:22:29
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Generation of solitons in media with arbitrary degree of nonlocality using an optimization procedure
摘要： Using a recently developed technique based on the Rayleigh-Ritz optimization principle, we generate solitons for media with an arbitrary degree of nonlocality. We demonstrate that it is possible to obtain a plethora of complex self-trapped beams using known solutions to the harmonic oscillator for one-dimensional (1D), 2D, and 3D systems, but working directly with a generalized nonlinear nonlocal Schr?dinger equation. We compare the parameters obtained variationally between the phenomenological Gaussian response and other more realistic nonlocal responses. We report that, for both kinds of nonlocal models, our approach obtains variational solutions that can remain self-trapped for certain conditions. We corroborate that, in general, the soliton dynamics can be different between the Gaussian response and the more realistic media for an arbitrary degree of nonlocality.
关键词： nonlinear Schr?dinger equation,variational approximation,nonlocality,solitons,optical beams
更新于2025-09-23 15:22:29
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The coupled derivative nonlinear Schr??dinger equation: conservation laws, modulation instability and semirational solutions
摘要： For exploring the coupled derivative nonlinear Schr?dinger (DNLS) equation more systematically, we give the in?nitely many conservation laws of it. Then, the modulation instability of the plane wave solutions for the coupled system is discussed. The higher-order semirational solutions, which can be completely classi?ed as three types, for the coupled DNLS equation are constructed by utilizing the particular vector solutions of the Lax pair and the Darboux transformation.
关键词： Semirational solutions,Modulation instability,The coupled derivative nonlinear Schr?dinger equation,Darboux transformation,Conservation laws
更新于2025-09-23 15:21:01
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Configurational entropy of optical bright similariton in tapered graded-index waveguide
摘要： Con?gurational entropy (CE) consists of a family of entropic measures of information used to describe the shape complexity of spatially-localized functions with respect to a set of parameters. We obtain the Differential Con?gurational Entropy (DCE) for similariton waves traveling in tapered graded-index optical waveguides modeled by a generalized nonlinear Schr?dinger equation. It is found that for similariton’s widths lying within a certain range, DCE attains minimum saturation values as the nonlinear wave evolves along the effective propagation variable ζ (t). In particular, saturation is achieved earlier for lower values of the width, which we show correspond to global minima of the DCE. Such low entropic values lead to minimum dispersion of momentum modes as the similariton waves propagate along tapered graded-index waveguides, and should be of importance in guiding their design.
关键词： Optical ?ber communications,Tapered graded-index waveguide,Bright similariton,Con?gurational entropy,Generalized nonlinear Schr?dinger equation
更新于2025-09-23 15:21:01
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Towards a quantum time mirror for non-relativistic wave packets
摘要： We propose a method—a quantum time mirror (QTM)—for simulating a partial time-reversal of the free-space motion of a non-relativistic quantum wave packet. The method is based on a short-time spatially homogeneous perturbation to the wave packet dynamics, achieved by adding a nonlinear time-dependent term to the underlying Schr?dinger equation. Numerical calculations, supporting our analytical considerations, demonstrate the effectiveness of the proposed QTM for generating a time-reversed echo image of initially localized matter-wave packets in one and two spatial dimensions. We also discuss possible experimental realizations of the proposed QTM.
关键词： quantum wave packets,quantum time mirrors,quantum scattering,matter waves,nonlinear Schr?dinger equation
更新于2025-09-23 15:21:01
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Integrable Nonlocal PT Symmetric and Reverse Space-Time Nonlinear Schr?dinger Equations
摘要： In this chapter a review of recent advances related to the emerging ?eld of integrable nonlocal nonlinear P T symmetric, reverse space-time and reverse time only equations is presented. Starting from the well-known AKNS theory, it is shown how to obtain a host of nonlocal integrable equations previously discovered by the authors. Included are the nonlocal P T symmetric (1 + 1)D nonlinear Schr?dinger (NLS) equation and its multi-component generalization; the reverse space-time and reverse time only NLS equations along with their vector versions. The inverse scattering transform associated with the nonlocal NLS hierarchy is brie?y summarized and one soliton solutions corresponding to each of the above case are presented. The discrete nonlocal P T symmetric, reverse space-time and reverse time only NLS equations are also discussed. Starting from the Ablowitz-Ladik scattering problem, it is shown that all these discrete models arise from simple symmetry reductions.
关键词： nonlocal nonlinear Schr?dinger equation,reverse space-time,soliton solutions,reverse time,P T symmetry,integrable systems
更新于2025-09-23 15:21:01
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Outset of multiple soliton solutions to the nonlinear Schr?dinger equation and the coupled Burgers equation
摘要： The nonlinear Schr?dinger equation and the coupled Burgers equation illustrate the status of quantum particles, shock waves, acoustic transmission and traffic flow. Therefore these equations are physically significant in their own right. In this article, the new auxiliary equation method has been contrivanced in order to rummage exact wave solutions to previously stated nonlinear evolution equations (NLEEs). We have developed ample soliton solutions and have to do with the physical importance of the acquired solutions by setting the specific values of the embodied parameters through portraying figures and deciphered the physical phenomena. It has been established that the executed method is powerful, skilled to examine NLEEs, compatible to computer algebra and provides further general wave solutions. Thus, the investigation of exact solutions to other NLEES through the new auxiliary method is prospective and deserves further research.
关键词： the nonlinear Schr?dinger equation,the new auxiliary equation method,soliton,the coupled Burgers equation
更新于2025-09-23 15:19:57