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Symplectic schemes and symmetric schemes for nonlinear schr¨odinger equation in the case of dark solitons motion

International Journal of Modeling, Simulation, and Scientific Computing 2021年第6期12卷 150-167页

作者： Yiming Yao Miao Xu Beibei Zhu Quandong Feng College of Science Beijing Forestry University Beijing 100083P.R.China School of Mathematics and Physics University of Science and Technology Beijing Beijing 100083 P.R.China

In this paper,symplectic schemes and symmetric schemes are presented to simulate Nonlinear schrodinger equation(NLSE)in case of dark soliton ***,by Ablowitz–Ladik model(A–L model),the NLSE is discretized into a non-canonical Hamiltonian ***,different kinds of coordinate transformations can be used to standardize the non-canonical Hamiltonian ***,the symplectic schemes and symmetric schemes can be employed to simulate the solitons motion and test the preservation of the invariants of the A–L model and the conserved quantities approximations of the original *** numerical experiments show that symplectic schemes and symmetric schemes have similar simulation effect,and own significant superiority over non-symplectic and non-symmetric schemes in long-term tracking the motion of solitons,preserving the invariants and the approximations of conserved ***,it is obvious that coordinate transformations with more symmetry have a better simulation effect.

关键词： Symplectic schemes symmetric schemes nonlinear schr¨odinger equation dark solitons motion Ablowitz–Ladik model

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Effective regulation of the interaction process among three optical solitons

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Chinese Physics B 2024年第10期33卷 190-197页

作者： Houhui Yi Xiaofeng Li Junling Zhang Xin Zhang Guoli Ma School of Intelligent Manufacturing Weifang University of Science and TechnologyWeifang 262700China School of Aviation and Aerospace Tianjin Sino-German University of Applied SciencesTianjin 300350China

The interaction between three optical solitons is a complex and valuable research direction,which is of practical application for promoting the development of optical communication and all-optical information processing *** this paper,we start from the study of the variable-coefficient coupled higher-order nonlinear Schodinger equation(VCHNLSE),and obtain an analytical three-soliton solution of this *** on the obtained solution,the interaction of the three optical solitons is explored when they are incident from different initial velocities and *** the higher-order dispersion and nonlinear functions are sinusoidal,hyperbolic secant,and hyperbolic tangent functions,the transmission properties of three optical solitons before and after interactions are ***,this paper achieves effective regulation of amplitude and velocity of optical solitons as well as of the local state of interaction process,and interaction-free transmission of the three optical solitons is obtained with a small *** relevant conclusions of the paper are of great significance in promoting the development of high-speed and large-capacity optical communication,optical signal processing,and optical computing.

关键词： optical solitons solitons interactions nonlinear schr¨odinger equation higher-order dispersion and nonlinear effects

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Solitons in One-Dimensional Bose–Einstein Condensate with Higher-Order Interactions

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Communications in Theoretical Physics 2017年第11期67卷 623-626页

作者：王颖王炜周蜀渝 School of Science Jiangsu University of Science and Technology Institute of Photonics and Quantum Sciences School of Engineering and Physical Sciences Heriot-Watt University Key Laboratory for Quantum Optics Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences

We model a one-dimensional Bose–Einstein condensate with the one-dimensional Gross–Pitaevskii equation(1 D GPE) incorporating higher-order interaction effects. Based on the F-expansion method, we analytically solve the1 D GPE, identifying the typical soliton solution under certain experimental settings within the general wave-like solution set, and demonstrating the applicability of the theoretical treatment that is employed.

关键词： nonlinear schr¨odinger equation higher-order nonlinearity soliton

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Numerical Calculation of Monotonicity Properties of the Blow-Up Time of NLS

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Communications in Computational Physics 2009年第2期5卷 745-759页

作者： Hans Peter Stimming Wolfgang Pauli Institute c/o Institut fur MathematikUniversitat WienBotzmanngasse 91090 WienAustria

We investigate blow-up of the focusing nonlinear schr¨odinger equation,in the critical and supercritical *** simulations are performed to examine the dependence of the time at which blow-up occurs on properties of the data or the *** cases are considered:dependence on the scale of the nonlinearity when the initial data are fixed;dependence upon the strength of a quadratic oscillation in the initial data when the equation and the initial profile are fixed;and dependence upon a damping factor when the initial data are *** most of these situations,monotonicity in the evolution of the blow-up time does not occur.

关键词： nonlinear schr¨odinger equation finite time blow-up wave collapse

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