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Communications in Theoretical Physics 2018年第5期69卷 551-557页

作者： Zhong Du Bo Tian Xiao-Yu Wu and Yu-Qiang Yuan State Key Laboratory of Information Photonics and Optical Communications and School of Science Beijing University of Posts and Telecommunications Beijing 100876 China

Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue *** the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.

关键词： graded-index waveguide (2+l)-dimensional coupled nonlinear Schrodinger system similarity transformation rogue waves variable coefficients

Polynomial Decay and Blow Up of Solutions for variable coefficients Viscoelastic Wave Equation with Acoustic Boundary Conditions

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Acta Mathematica Sinica,English Series 2016年第2期32卷 153-174页

作者： Yamna BOUKHATEM Benyattou BENABDERRAHMANE Laboratory of Computer Sciences and Mathematics Faculty of SciencesUniversity of LaghouatP.O.BOX 37GLaghouat(03000)Algeria Faculty of Mathematics and Computer Sciences University of M'SilaAlgeria

A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.

关键词： Acoustic boundary conditions blow up polynomial decay variable coefficients viscoelas-tic wave equation

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF variable coefficients WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2017年第5期37卷 1453-1471页

作者： Vamna BOUKHATEM Benyattou BENABDERRAHMANE Laboratory of Pure and Applied Mathematics University of LaghouatP.O.Box 37GLaghouat 03000Algeria Laboratory of Pure and Applied Mathematics Mohamed Boudiaf UniversityM'sila 28000Algeria

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is *** suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

关键词： acoustic boundary conditions general decay time-varying delay variable coefficients viscoelastic equation

A Kernel-Free Boundary Integral Method for variable coefficients Elliptic PDEs

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Communications in Computational Physics 2014年第4期15卷 1108-1140页

作者： Wenjun Ying Wei-Cheng Wang Department of Mathematics MOE-LSC and Institute of Natural SciencesShanghai Jiao Tong UniversityMinhangShanghai 200240P.R.China Department of Mathematics National Tsing Hua Universityand National Center for Theoretical SciencesHsinChu300Taiwan

This work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations(PDEs),including both boundary value and interface *** method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral *** of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution,which satisfies an equivalent discrete interface problem,while the interface problem is solved by a fast solver in the Cartesian *** computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the *** paper gives implementation details for a secondorder version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface *** interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem,where the elliptic PDEs on two sides of the interface are of different types.

关键词： Elliptic partial differential equation variable coefficients kernel-free boundary integral method finite difference method geometric multigrid iteration

Identification of variable coefficients for vibrating systems by boundary control and observation

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控制理论与应用（英文版） 2008年第2期6卷 127-132页

作者： Jinde CHANG Academy of Mathematics and Systems Science Academia Sinica Beijing 100080 China Graduate University of Chinese Academy of Sciences Beijing 100049 China

We consider the identification problem of coefficients for vibrating systems described by a Euler-Bernoulli beam eq~. ation Or a string equation, with one end clamped and with an input exerted on the other end. For the beam equation, the observations are the velocity and the angle velocity at the free end, while for the string equation, the observation is the velocity at the free end. In the framework of well-posed linear system theory, we show that both the density and the flexural rigidity of the beam, and the tension of the string, can be uniquely determined by the observations for all positive times. Moreover, a general constructive method is developed to show that the mass density and the elastic modulus of the string are not determined by the observation.

关键词： Beam equation Identifiability Well-posedness variable coefficients Inverse problem

A Formula of General Solution for a Class of Homogeneous Trinomial Recurrence of variable coefficients with Two Indices

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Wuhan University Journal of Natural Sciences 2005年第5期10卷 828-832页

作者： YU Dan YU Chang-an School of Computer Wuhan University Wuhan 430072 Hubei China School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China

In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.

关键词： a formula of general solution homogeneous trinomial recurrence variable coefficients two indices

A Constraction of General Solution for a Class of Non-Homogeneous Recurrence of variable coefficients with Two Indices

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Wuhan University Journal of Natural Sciences 2000年第4期5卷 379-385页

作者： Yu Chang-an College of Mathematics and Computer Science, Wuhan University, Wuhan 430072,China College of Mathematics and Computer Science Wuhan UniversityWuhan 430072China

In this paper, we obtain an explicit formula of general solution for a class of the non-homogeneous recurrence of variable coefficients with two indices.

关键词： two indices variable coefficients non homogeneous recurrence explicit solution

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with variable coefficients

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Engineering（科研） 2021年第6期13卷 306-329页

作者： Yanmeng Sun Qing Yang School of Mathematics and Statistics Shandong Normal University Jinan China

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

关键词： Two-Dimensional First-Order Hyperbolic Equation variable coefficients Upwind Difference Schemes Fourier Method Stability and Error Estimation

Permanence and Periodic Solution of an Impulsive Delay Two-prey One-predator System with variable coefficients

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Chinese Quarterly Journal of Mathematics 2009年第2期24卷 267-273页

作者： LIU Yan-wei LU Kai-zhang Department o.f Mathematics Zhoakou Normal University Zhoukou 466001 China

two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.

关键词： impulsive delay comparison principle variable coefficients

New Exact Solutions for the Generalized （2 ＋ 1）-dimensional Nonlinear Schroedinger Equation with variable coefficients

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Chinese Quarterly Journal of Mathematics 2012年第2期27卷 224-231页

作者： JIANG Zhi-ping Center for Teaching and Learning Development Zhejiang International Studies University Hangzhou310012 China

With the help of the variable-coefficient generalized projected Ricatti equation expansion method, we present exact solutions for the generalized （2＋1）-dimensional nonlinear SchrSdinger equation with variable coefficients. These solutions include solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time.

关键词： (2+1)-dimensions nonlinear SchrSdinger equation variable coefficients projected Ricatti equation expansion method