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exact Solutions of Nonlinear Evolution Equations in Mathematical Physics Using the Modified Simple Equation Method

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Chinese Physics Letters 2012年第6期29卷 1-4页

作者： E.M.E.Zayed S.A.Hoda Ibrahim Department of Mathematics Faculty of ScienceZagazig UniversityP.O.Box 44519ZagazigEgypt

The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction-diffusion *** these parameters are taken to be special values,the solitary wave solutions are derived from the exact *** is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

关键词： equation. exact equation

exact Analytic Solutions for a Finite Width Strip with a Single Edge Crack

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Chinese Physics Letters 1999年第1期16卷 32-34页

作者： FAN Tian-you YANG Xiao-chun LI He-xin Research Center of Materials Science Beijing Institute of TechnologyBeijing 100081

The present study develops a conformal mapping technique and deals with the exact analytic solutions in closed form to the finite width strip with single edge *** exact solutions including a universal suitable constan... 详细信息

关键词： exact conformal analytic

exact Treatment of l≠0 States

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Chinese Physics Letters 2004年第9期21卷 1685-1688页

作者： B.Gonul DepartmentofEngineeringPhysics FacultyofEngineeringUniversityofGaziantep27310Gaziantep-Turkiye

Using the basic ingredient of supersymmetry, we present a general procedure for the treatment of quantum states having nonzero angular momenta.

关键词： Chpher(0) Nonzero Angle Countries (nations) QUANTUM STATES Angular momentum supersymmetry exact

exact Vortex Clusters of Two-Dimensional Quantum Fluid with Harmonic Confinement

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Chinese Physics Letters 2013年第4期30卷 14-17页

作者： CHONG Gui-Shu ZHANG Ling-Ling HAI Wen-Hua School of Physics and Microelectronics Hunan UniversityChangsha 410082 Department of Physics and Key Laboratory of Low-Dimensional Quantum Structure and Quantum Control of Ministry of Education Hunan Normal UniversityChangsha 410081

A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schr?dinger equation is presented,which describes different kinds of vortex *** dynamics of different vortex clusters,such as the single vortex,vortex pair,vortex dipole and vortex trimer in a two-dimensional quantum fluid are analytically studied based on these exact *** time evolutions of the wave of such vortices are demonstrated,and the orbits of motion of singular points in the vortices are also *** interactions of vortices in many-vortex clusters are discussed.A repulsive interaction between vortices with the same topological charge,and inter-annihilation and inter-creation of vortices with opposite topological charge,are shown.

关键词： vortex exact topological

exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe

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Science China(Physics,Mechanics & Astronomy) 2005年第4期48卷 485-495页

作者： TONG Dengke WANG Ruihe YANG Heshan Institute of Mathematics and Computional Science University of Petroleum Beijing 102249 China Institute of Mathematics and Computional Science University of Petroleum Beijing 102249 China Institute of Mathematics and Computional Science University of Petroleum Beijing 102249 China

This paper deals with some unsteady unidirectional transient flows of Oldroyd-B fluid in an annular pipe. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. exact solutions of some unsteady flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. The following four problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in an annulus; (3) axial Couette flow in an annulus due to a longitudinal constant shear; (4) Poiseuille flow due to a constant pressure gradient and a longitudinal constant shear. The well-known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appear as limited cases of our solutions.

关键词： fractional calculus, generalized Oldroyd-B fluid, exact solutions, velocity fields.

exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

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Science China(Technological Sciences) 2009年第8期52卷 2424-2431页

作者： HUANG ZhiLong1,2 & JIN XiaoLing1 1 Department of Mechanics, Zhejiang University, Hangzhou 310027, China 2 The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China Department of Mechanics Zhejiang University Hangzhou 310027 China The State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

A new procedure is proposed to construct strongly nonlinear systems of multiple degrees of freedom subjected to parametric and/or external Gaussian white noises, whose exact stationary solutions are independent of energy. Firstly, the equivalent Fokker-Planck-Kolmogorov (FPK) equations are derived by using exterior differentiation. The main difference between the equivalent FPK equation and the original FPK equation lies in the additional arbitrary antisymmetric diffusion matrix. Then the exact stationary solutions and the structures of the original systems can be obtained by using the coefficients of antisymmetric diffusion matrix. The obtained exact stationary solutions, which are generally independent of energy, are for the most general class of strongly nonlinear stochastic systems multiple degrees of freedom (MDOF) so far, and some classes of the known ones dependent on energy belong to the special cases of them.

关键词： exact stationary solution nonlinear stochastic system equivalent system independent of energy

exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (Ⅰ)——exact solutions for piezoelectric circular plate

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Science China(Technological Sciences) 1999年第4期42卷 388-395页

作者：丁皓江徐荣桥国凤林 1. Department of Civil Engineering Zhejiang University 310027 Hangzhou China

Based on three-dimensional elastic equations for piezoelectric materials, the state equations for piezoelectric circular plate under axisymmetric deformation are derived. Applying Hankel transform to them and letting the free boundary terms resulting from Hankel transform be zero, a set of ordinary differential equations with constant coefficients and associated boundary conditions are obtained. Furthermore, two exact solutions corresponding to generalized rigid slipping and generalized elastic simple support are deduced. Then, the governing equations obtained reduce to equations for axisymmetric problem of transversely isotropic circular plate. Under the two types of boundary conditions of elastic simple support and rigid slipping, exact solutions are derived. Finally, numerical results are presented and applicability of the classical plate theory is discussed.

关键词： transversely isotropy axisymmetric deformation exact solution piezoelectric circular plate.

exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States

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Communications in Theoretical Physics 2019年第5期71卷 623-628页

作者： You-Fei Xie Qing-Hu Chen Department of Physics Zhejiang UniversityHangzhou310027China Collaborative Innovation Center of Advanced Microstructures Nanjing UniversityNanjing210093China

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling is present on an equal footing, is studied within the tunable extended coherent states. The eigenvalues and eigenstates are therefore obtained exactly. Surprisingly, the entanglement entropy in the ground-state is found to jump suddenly with the coupling strength. The first-order quantum phase transition can be detected by level crossing of the ground state and the first excited state, which is however lacking in the original linear quantum Rabi model. Performing the first-order approximation in the present theory, we can derive closed-form analytical results for the ground-state. Interestingly, it agrees well with the exact solutions up to the ultra-strong coupling regime in a wide range of model parameters. The spectral collapses when the absolute value of the nonlinear coupling strength approaches to twice the cavity frequency is observed with the help of new solutions in the limits.

关键词： extended coherent states exact eigenvalues first-order phase transitions spectral collapse

Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media

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Frontiers of Structural and Civil Engineering 2019年第1期13卷 201-214页

作者： Jaroon RUNGAMORNRAT Chung Nguyen VAN Applied Mechanics and Structures Research Unit Department of Civil EngineeringFaculty of EngineeringChulalongkorn UniversityBangkok 10330Thailand Faculty of Civil Engineering Ho Chi Minh City of Technology and EducationHo Chi Minh 721400Vietnam

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional,linear,second-order,boundary value problems with a domain completely described by a circular defining *** scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems,bounded and unbounded bodies,distributed body source,*** boundary conditions to be treated in a unified *** conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve,exact geometry of the domain,and exact spatial differential *** finite element shape functions are employed in the discretization of both trial and test functions in the circumferential direction and the resulting eigenproblem is solved by a selected efficient *** computational performance of the implemented procedure is then fully investigated for various scenarios to demonstrate the accuracy in comparison with standard linear elements.

关键词： multi-field problems defining curve exact geometry general boundary conditions SBFEM