- 标题
- 摘要
- 关键词
- 实验方案
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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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Dynamical distortions of structural signatures in molecular high-order harmonic spectroscopy
摘要： We study the signature of two-center interferences in molecular high-order harmonic spectra, with an emphasis on the spectral phase. With the help of both ab initio computations based on the time-dependent Schr?dinger equation and the molecular strong-field approximation (SFA) as developed by Chiril? et al. [Phys. Rev. A 73, 023410 (2006)] and Faria [Phys. Rev. A 76, 043407 (2007)], we observe that the phase behavior is radically different for the short and the long trajectory contributions. By means of Taylor expansions of the molecular SFA, we link this effect to the dynamics of the electron in the continuum. More precisely, we find that the value of the electric field at recombination time plays a crucial role in the shape of the destructive interference phase jump.
关键词： molecular spectroscopy,spectral phase,strong-field approximation,two-center interferences,time-dependent Schr?dinger equation,high-order harmonic generation
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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Introducing a quantum kinetic model using the generalized Boltzmann equation in the complex phase space
摘要： In the present work, using the generalized Boltzmann equation of the ?rst author [Phys. Rev. E 94, 023316 (2016)], a quantum kinetic model in the complex phase space is proposed. Employing the Chapman-Enskog analysis and applying the Wick rotation (using complex-valued relaxation time), it is shown that the present model recovers the time-dependent Schr?edinger equation, while preserving the main features of the conventional lattice Boltzmann models, e.g., simplicity of implementation, second-order accuracy (in space), and convenience in parallel programming. The present results are numerically veri?ed by simulating three benchmark problems.
关键词： quantum kinetic model,Schr?dinger equation,Wick rotation,lattice Boltzmann models,generalized Boltzmann equation,Chapman-Enskog analysis,complex phase space
更新于2025-09-23 15:21:21
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Optical Gaussons for nonlinear logarithmic Schr?dinger equations via the variational iteration method
摘要： In this work, we study the logarithmic Schr?dinger equation, with and without a detuning term. We derive optical Gaussons, named for their Gaussian shape, for these logarithmic models via using the variational iteration method. The obtained Gaussons are characterized by no soliton radiation, and propagate through dispersion-managed optical fibers. The physical structures of the derived Gaussons, namely, its amplitude and width will be examined for a variety numerical values of the parameters.
关键词： Schr?dinger equation,Logarithmic nonlinearity,Optical fibers,Gaussons
更新于2025-09-23 15:21:21
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On short-range pulse propagation described by (2 + 1)-dimensional Schr??dinger's hyperbolic equation in nonlinear optical fibers
摘要： The (2 + 1)-dimensional Schr?dinger complex equations are essential physical models that describe the short-range pulse spread in nonlinear media fiber optics. We construct novel complex solutions to Schr?dinger’s complex hyperbolic model by using two different techniques. One method is characterized by the efficient algebraic equations that eventually form. Meanwhile, it uses the dependency variable expressions and its derivatives in the differential equation of the polynomial of a solitary wave. New acquired solutions are rational and exponential solutions expressed by periodic solutions. The solutions are illustrated through 3D- and 2D- plots to clarify the physical features for this model.
关键词： New soliton solutions,Hyperbolic (2 + 1)- dimensional Schr?dinger equation,Complex transformation
更新于2025-09-23 15:21:01
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Ring modes supported by concentrated cubic nonlinearity
摘要： We consider the one-dimensional Schr?dinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, con?ned to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the nonlinearity coef?cient represented by the δ function, all stationary states are obtained in an exact analytical form. The states with positive chemical potentials are found in alternating bands for the cases of the self-repulsion and attraction, while solutions with negative chemical potentials exist only in the latter case. These results provide a possibility to obtain exact solutions for band-gap states in the nonlinear system. Approximating the δ function by a narrow Gaussian, stability of the stationary modes is addressed through numerical computation of eigenvalues for small perturbations, and veri?ed by simulations of the perturbed evolution. For positive chemical potentials, the stability is investigated in three lowest bands. In the case of the self-attraction, each band contains a stable subband, the transition to instability occurring with the increase of the total norm. As a result, multipeak states may be stable in higher bands. In the case of the self-repulsion, a single-peak ground state is stable in the ?rst band, while the two higher ones are populated by weakly unstable two- and four-peak excited states. In the case of the self-attraction and negative chemical potentials, single-peak modes feature instability which transforms them into persistently oscillating states.
关键词： cubic nonlinearity,Bose-Einstein condensates,stationary states,optics,Schr?dinger equation,stability analysis
更新于2025-09-23 15:21:01