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Attractors and Dimensions for Discretizations of a nls equation with a Non-local Nonlinear Term

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Acta Mathematica Sinica,English Series 2002年第4期18卷 779-800页

作者： Shu Qing MA Qian Shun CHANG Department of Mathematics Science. University of Alberta. Canada T6G 2G1 Institute of Applied Mathematics. Academy of Mathematics and System Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. China Department of Mathematics Science University of Alberta Alberta Canada T6G 2G1 Institute of Applied of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing P. R. China

In this paper we consider a semi-dicretized nonlinear Schrdinger (nls) equation with local integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds tor the Hausdorff and fractal dimensions of the discrete attractors are obtained, and the various bounds are independent of the mesh sizes. Furthermore. numerical experiments are given and many interesting phenomena are observed such as limit cycles, chaotic attractors and a so-called crisis of the chaotic attractors.

关键词： Attractor nls equation

The Fifth Order Peregrine Breather and Its Eight-Parameter Deformations Solutions of the nls equation

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Communications in Theoretical Physics 2014年第3期61卷 365-369页

作者： Pierre Gaillard Unversitéde Bourgogne Campus de Mirande 9 Avenue Alain Savary

We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real *** gives new families of quasi-rational solutions of the nls equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.

关键词： nls equation Peregrine breathers Akhmediev's solutions

A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of nls equation with Singular Potential

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Analysis in Theory and Applications 2017年第4期33卷 333-354页

作者： Riadh Chteoui Anouar Ben Mabrouk Departement de Mathmatiques Facult des Sciences de TunisUniversit de Tunis ElManar UR11ES50–Algebra Number Theory and Nonlinear Analysis Department ofMathematics Faculty of Sciences Monastir University Department of Mathematics Higher Institute of Applied Mathematics andInformatics Street of Assad Ibn Alfourat Kairouan University Department of Mathematics College of Sciences University of Tabuk

In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.

关键词： nls equation finite-difference scheme stability analysis Lyapunov criterion con-sistency convergence error estimates Lyapunov operator.

PERTURBATION ANALYSIS FOR WAVE equation OF NONLINEAR ELASTIC ROD

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Applied Mathematics and Mechanics(English Edition) 2006年第9期27卷 1233-1238页

作者：吕克璞郭鹏张磊易金桥段文山 College of Physics and Electronic Engineering Northwest Normal University Lanzhou 730070 P. R. China

The longitudinal oscillation of a nonlinear elastic rod with lateral inertia was studied. Based on the far field and simple wave theory, a nonlinear SchrSdinger （nls） equation was established under the assumption of small amplitude and long wavelength. It is found that there are nls envelop solitons in this system. Finally the soliton solution of the nls equation was presented.

关键词： nonlinear elastic rod far field nls equation

The nonlinear evolution of rogue waves generated by means of wave focusing technique

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Science China(Physics,Mechanics & Astronomy) 2011年第1期54卷 35-41页

作者： HU HanHong MA Ning School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University Shanghai 200240 China

Generating the rogue waves in offshore engineering is investigated,first of all,to forecast its occurrence to protect the offshore structure from being attacked,to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure *** achieve these purposes demands an accurate wave generation and *** this paper,we establish a spatial domain model of fourth order nonlinear Schrdinger(nls) equation for describing deep-water wave trains in the moving coordinate *** order to generate rogue waves in the experimental tank efficiently,we take care that the transient water wave(TWW) determines precisely the concentration of time/*** we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University(SJTU) under the linear superposing *** discuss its nonlinearity for guiding the experiment,we set the TWW as the initial condition of the nls *** differences between the linear and nonlinear simulations are ***,the characteristics of the transient water wave,including water particle velocity and wave slope,are investigated,which are important factors in safeguarding the offshore structures.

关键词： nls equation transient water wave water velocity wave slope

Exact Analytical Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

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Communications in Theoretical Physics 2007年第1期47卷 143-148页

作者： CHEN Yong LI Biao ZHENG Yu Nonlinear Science Center and Department of Mathematics Ningbo University Ningbo 315211 China Department of Mathematics East China Normal University Shanghai 200062 China MM Key Lab the Chinese Academy of Sciences Beijing 100080 China

In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.

关键词： nls equation soliton symbolic computation

Assessment of theoretical approaches to derivation of internal solitary wave parameters from multi-satellite images near the Dongsha Atoll of the South China Sea

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Acta Oceanologica Sinica 2022年第6期41卷 137-145页

作者： Huarong Xie Qing Xu Quanan Zheng Xuejun Xiong Xiaomin Ye Yongcun Cheng Key Laboratory of Marine Hazards Forecasting of Ministry of Natural Resources Hohai UniversityNanjing 210098China College of Marine Technology Faculty of Information Science and EngineeringOcean University of ChinaQingdao 266100China Department of Atmospheric and Oceanic Science University of MarylandCollege ParkMaryland 20742USA First Institute of Oceanography Ministry of Natural ResourcesQingdao 266061China National Satellite Ocean Application Service State Oceanic AdministrationBeijing 100081China Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou) Guangzhou 511458China PIESAT Information Technology Co. Ltd.Beijing 100195China

This study assesses the accuracy and the applicability of the Korteweg-de Vries(KdV)and the nonlinear Schr?dinger(nls)equation solutions to derivation of dynamic parameters of internal solitary waves(ISWs)from satellite *** band images taken by five satellite sensors with spatial resolutions from 5 m to 250 m near the Dongsha Atoll of the northern South China Sea(NSCS)are used as a *** the baseline,the amplitudes of ISWs occurring from July 10 to 13,2017 are estimated by the two approaches and compared with concurrent mooring observations for *** the ratio of the dimensionless dispersive parameter to the square of dimensionless nonlinear parameter as a criterion,the best appliable ranges of the two approaches are clearly *** statistics of total 18 cases indicate that in each 50%of cases,the KdV and the nls approaches give more accurate estimates of ISW *** is found that the relative errors of ISW amplitudes derived from two theoretical approaches are closely associated with the logarithmic bottom *** may be attributed to the nonlinear growth of ISW amplitudes as propagating along a shoaling thermocline or *** test results using three consecutive satellite images to retrieve the ISW propagation speeds indicate that the use of multiple satellite images(>2)may improve the accuracy of retrieved phase ***,repeated multi-satellite images of ISWs can help to determine the types of ISWs if mooring data are available nearby.

关键词： internal solitary waves KdV equation nls equation South China Sea satellite images

Dark solitons in nonlinear-optical fibers

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光通信技术 1998年第2期 173-176页

作者： Zhang Jingsong Wang Zhi Zhao Yucheng Jian Shuisheng(Institute of Lightwave Technology Northern Jiaotong University,Beijing, 100044)

Using method of separation of variables,we resolve nonlinear Schrbdinger equation in the normal-dispersion regime of an optical fiber. The phase form of the darksolitons in this paper is different from that in previou... 详细信息

关键词： Dark solitons nls equation GVD

Financial Rogue Waves

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Communications in Theoretical Physics 2010年第11期 947-949页

作者：闫振亚 Key Laboratory of Mathematics Mechanization Institute of Systems ScienceAMSSChinese Academy of Sciences

We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes *** rogue wave solutions may be used to describe thepossib... 详细信息

关键词： nls equation nonlinear option pricing model financial rogue waves