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Exact optical solitons in metamaterials with anti-cubic law of nonlinearity by Lie group method
摘要： In this paper, using Lie point symmetry analysis, we study the dynamics of the solitons for the nonlinear Schrodinger’s equation with anti-cubic nonlinearity. Some new doubly periodic solutions are obtained that degenerate to dark and bright soliton solutions. In our of best knowledge, the obtained solutions are new. Those obtained results have important applications in the understanding the nonlinear propagation theory of solitons in metamaterials.
关键词： Schrodinger’s equation,Soliton solutions,Lie symmetry analysis
更新于2025-09-23 15:23:52
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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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Generalization of optical solitons with dual dispersion in the presence of Kerr and quadratic-cubic law nonlinearities
摘要： In this work, nonlinear Schr?dinger’s equation along with group velocity dispersion and spatio-temporal dispersion is considered in (n + 1) dimensions with Kerr and quadratic-cubic law nonlinearities which expose the propagation of light pulses in fiber optics. Dark, singular and periodic singular optical solitons in (n + 1) dimensions are retrieved and generalized through versatile modified simple equation method. The constraint conditions that righteously guarantee the perseverance of these soliton solutions are obtained as an outgrowth. The results presented in this paper are new and generalized which are already available in the literature.
关键词： constraints,(n + 1)-dimensional nonlinear Schr?dinger’s equation,modified simple equation 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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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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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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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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[IEEE 2018 2nd International Conference on Electronics, Materials Engineering & Nano-Technology (IEMENTech) - Kolkata (2018.5.4-2018.5.5)] 2018 2nd International Conference on Electronics, Materials Engineering & Nano-Technology (IEMENTech) - Effect of Self-Consistency Technique on Current Density Profile of Resonant Tunneling Diode
摘要： This paper reveals the importance of self-consistency technique for computing current density in resonant tunneling device. AlxGa1-xAs/GaAs/AlyGa1-yAs is considered for simulation purpose, and both Schr?dinger and Poisson's equations are simultaneously solved subject to appropriate boundary conditions to obtain current density as a function of externally applied bias. Structural parameters and material compositions within type-I range are varied to get the fluctuations in current, which is otherwise absent when calculation is performed without applying self-consistency technique. Findings are significant as magnitude of current obtained is higher than that obtained when self-consistency is absent. Result has immense importance for low bias application of RTD due to the presence of peaks at particular system compositions.
关键词： Peak current density,Resonant tunneling diode,Poisson's equation,Current density,Self-consistency technique,Schrodinger's equation
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