期刊文献+
共找到25篇文章
< 1 2 >
每页显示 20 50 100
On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids 被引量:5
1
作者 侯国林 阿拉坦仓 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第8期2753-2758,共6页
The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular dom... The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method. 展开更多
关键词 magnetoelectroelastic solid variable separation method COMPLETENESS general solution
下载PDF
A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM
2
作者 Yan Xianggan Wu Jike, Department of Mechanics, Peking Unirersity, Bejing 100871. China 《Acta Mechanica Solida Sinica》 SCIE EI 1997年第3期255-261,共7页
By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution ... By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis. 展开更多
关键词 separation of singularity series resolution method of separation of variables boundary value problem characteristic equation
下载PDF
Solving mKdV-sinh-Gordon equation by a modified variable separated ordinary differential equation method 被引量:4
3
作者 谢元喜 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第12期5123-5132,共10页
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact sol... By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV-sinh-Gordon equation by this approach. 展开更多
关键词 modified variable separated ODE method mKdV-sinh-Gordon equation explicit andexact solution
下载PDF
Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method 被引量:1
4
作者 苏卡林 谢元喜 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第10期40-48,共9页
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equa... By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. 展开更多
关键词 modified variable separated ODE method (2 1)-dimensional sine-Poisson equation explicit and exact solution
下载PDF
Some discussions about method for solving the variable separating nonlinear models
5
作者 阮航宇 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第5期17-24,共8页
Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of th... Through analysing the exact solution of some nonlinear models, the role of the variable separating method in solving nonlinear equations is discussed. We find that rich solution structures of some special fields of these equations come from the nonzero seed solution. However, these nonzero seed solutions is likely to result in the divergent phenomena for the other field component of the same equation. The convergence and the signification of all field components should be discussed when someone solves the nonlinear equation using the variable separating method. 展开更多
关键词 variable separating method nonzero seed solution nonlinear equation
下载PDF
New Families of Rational Form Variable Separation Solutions to(2+1)-Dimensional Dispersive Long Wave Equations
6
作者 WEN Xiao-Yong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期789-793,共5页
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transfor... With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions. 展开更多
关键词 improved mapping approach variable separation method (2+1)-dimensional dispersive long wave equations symbolic computation
下载PDF
Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method
7
作者 Huwaida K.Elgweri Amal Hamed Mohamed Mansor 《Journal of Physical Science and Application》 2022年第1期12-18,共7页
The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method i... The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique. 展开更多
关键词 Finite difference time domain method diffusion equation separation of variables method finite well potential Schrödinger equation
下载PDF
Exactly solving some typical Riemann-Liouville fractional models by a general method of separation of variables
8
作者 Cheng-Shi Liu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第5期46-51,共6页
Finding exact solutions for Riemann–Liouville(RL)fractional equations is very difficult.We propose a general method of separation of variables to study the problem.We obtain several general results and,as application... Finding exact solutions for Riemann–Liouville(RL)fractional equations is very difficult.We propose a general method of separation of variables to study the problem.We obtain several general results and,as applications,we give nontrivial exact solutions for some typical RL fractional equations such as the fractional Kadomtsev–Petviashvili equation and the fractional Langmuir chain equation.In particular,we obtain non-power functions solutions for a kind of RL time-fractional reaction–diffusion equation.In addition,we find that the separation of variables method is more suited to deal with high-dimensional nonlinear RL fractional equations because we have more freedom to choose undetermined functions. 展开更多
关键词 Riemann–Liouville derivative exact solution fractional differential equation separation of variables method
原文传递
Analytical Solution for Thermal Flutter of Laminates in Supersonic Speeds
9
作者 Lintong Dai Qiaozhen Sun 《Journal of Applied Mathematics and Physics》 2020年第8期1525-1534,共10页
<div style="text-align:justify;"> As a basic component of engineering fields such as aeronautics, astronautics and shipbuilding, panel structure has been widely used in engineering and scientific resea... <div style="text-align:justify;"> As a basic component of engineering fields such as aeronautics, astronautics and shipbuilding, panel structure has been widely used in engineering and scientific research. It is of great theoretical and practical significance to study the vibration of panels. The panel flutter problem has caused widely concerned by researchers at home and abroad during to the emergence of high-speed aircrafts. With regard to the eigenvalue problem of rectangular panels, it is generally believed that it is difficult to obtain a closed form eigen solution in the case of an adjacent boundaries clamped-supported or a free boundary that cannot be decoupled. Aiming at the problem, this paper studies the two-dimensional symmetric orthogonal laminated plate structure in the hypersonic flow in the thermal environment, and combines the first-order piston aerodynamic theory to study a high-precision separation variable method. Through this method, analytical solution to the closed form of the thermal flutter problem of rectangular panels can be obtained under any homogeneous boundary conditions. </div> 展开更多
关键词 Two-Dimensional Panel Thermal Flutter separation variable method Analytical Solution
下载PDF
Wave Radiation and Diffraction by A Two-Dimensional Floating Body with An Opening Near A Side Wall 被引量:6
10
作者 张洪生 周华伟 《China Ocean Engineering》 SCIE EI CSCD 2013年第4期437-450,共14页
The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory... The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains. 展开更多
关键词 wave radiation and diffraction floating body with an opening side wall variable separation method domain decomposition
下载PDF
Analysis of steady heat conduction for 3D axisymmetric functionally graded circular plate 被引量:3
11
作者 刘五祥 《Journal of Central South University》 SCIE EI CAS 2013年第6期1616-1622,共7页
The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary d... The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation (ODE) in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored. 展开更多
关键词 functionally graded circular plate variable separation method steady heat conduction Peano-Baker series
下载PDF
Complex Wave Solutions for (2+1)-Dimensional Modified Dispersive Water Wave System 被引量:1
12
作者 LIANG Jin-Fu GONG Lun-Xun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第7期17-22,共6页
The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the (2+1)-dimensional modified... The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the (2+1)-dimensional modified dispersive water-wave (MDWW) system are obtained. Based on a derived periodic solitary wave solution and a rational solution, we study a type of phenomenon of complex wave. 展开更多
关键词 MDWW system generalized Riccati equation variable separation method complex wave
下载PDF
Exact Solutions to a Combined sinh-cosh-Gordon Equation 被引量:1
13
作者 魏龙 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第10期599-602,共4页
Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbo... Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation 展开更多
关键词 function transformation method variable separated ODE method combined sinh-cosh-Gordonequation
下载PDF
Solutions of novel soliton molecules and their interactions of(2+1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation 被引量:1
14
作者 Hong-Cai Ma Yi-Dan Gao Ai-Ping Deng 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第7期77-83,共7页
The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations.In this paper,we use a new form of variable separation to study novel soliton molecules and thei... The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations.In this paper,we use a new form of variable separation to study novel soliton molecules and their interactions in(2+1)-dimensional potential Boiti–Leon-Manna–Pempinelli equation.Dromion molecules,ring molecules,lump molecules,multi-instantaneous molecules,and their interactions are obtained.Then we draw corresponding images with maple software to study their dynamic behavior. 展开更多
关键词 variable separation method Hirota bilinear method dromion solution (2+1)-dimensional potential Boiti–Leon–Manna–Pempinelli equation
下载PDF
Doubly Periodic Propagating Wave Patterns of (2+1)-Dimensional Maccari System
15
作者 HUANG Wen-Hua LIU Yu-Lu MA Zheng-Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第3期397-402,共6页
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+ 1)-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd ... Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+ 1)-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed. 展开更多
关键词 Maccari system variable separation method Jacobi elliptic function periodic wave
下载PDF
Doubly Periodic Propagating Wave for (2+1)-Dimensional Breaking Soliton Equation
16
作者 HUANG Wen-Hua LIU Yu-Lu ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期268-274,共7页
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in... Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic. 展开更多
关键词 breaking soliton equation variable separation method Jabobi elliptic function periodic wave
下载PDF
Theoretical solution of a spherically isotropic hollow sphere for dynamic thermoelastic problems
17
作者 王惠明 丁皓江 陈伟球 《Journal of Zhejiang University Science》 EI CSCD 2003年第1期8-12,共5页
The separation of variables method was successfully used to resolve the spherically symmetric dynamic thermoelastic problem for a spherically isotropic elastic hollow sphere. Use of the integral transform can be avoid... The separation of variables method was successfully used to resolve the spherically symmetric dynamic thermoelastic problem for a spherically isotropic elastic hollow sphere. Use of the integral transform can be avoided by means of this method, which is also appropriate for an arbitrary thickness hollow sphere subjected to arbitrary thermal and mechanical loads. Numerical results are presented to show the dynamic stress responses in the uniformly heated hollow spheres. 展开更多
关键词 separation of variables method Spherically symmetric THERMOELASTIC Hollow sphere
下载PDF
New Exact Solutions and Localized Structures for (3+1)-Dimensional Burgers System
18
作者 LI Jiang-Bo MA Song-Hua REN Qing-Bao FANG Jian-Ping ZHENG Chun-Long 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第4期955-959,共5页
With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) ... With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons. 展开更多
关键词 extended mapping approach variable separation method (3+1)-dimensional Burgers system localized coherent structures the interactions between solitons
下载PDF
Restrained Bending of Thin-Walled Box Beam with Honeycomb Core
19
作者 臧庆来 张行 吴国勋 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第3期223-229,共7页
Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are e... Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of shearing force is formulated by trigonometric series and used to determine the coefficients in above expansions. The computational resuits give the chord and span wise distributions of nomal and shear stress in the cover plate and the honeycomb core. At the same time, the attenuation of additional stress from fixed end to free end along the length of beam is shown clearly. 展开更多
关键词 box beam HONEYCOMB restrained bending method of variable separation eigen function expansion
下载PDF
Restrained Torsion of Thin-walled Box Beam with Honeycomb Core
20
作者 臧庆来 张行 吴国勋 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第4期336-345,共10页
Restrained torsion of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are e... Restrained torsion of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of torque is formulated by trigonometric series and used to determine the coefficients in above expansions. The results of computation provide the chord-wise and span-wise distributions of normal and shear stress in the face plate along with shear stress in the honeycomb core. 展开更多
关键词 box beam HONEYCOMB restrained torsion method of variable separation eigen function expansion
下载PDF
上一页 1 2 下一页 到第
使用帮助 返回顶部