The Caudrey-Dodd-Gibbon-Kotera Sawada (CDGKS) equation has attracted many physicists and mathematicians. In this paper, based on the idea of variable-coefficient balancing-act method and the computerized .symbolic com...The Caudrey-Dodd-Gibbon-Kotera Sawada (CDGKS) equation has attracted many physicists and mathematicians. In this paper, based on the idea of variable-coefficient balancing-act method and the computerized .symbolic compu tation, some exact analytic solutions for the CDGKS equation have been obtained.展开更多
Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeabili...Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.展开更多
This paper presents a new method exactly to solve the bending of elastic thinplates with arbitrary shape. First the analytic solution of differential equation ofelastic thin plate is derived in polar coordinate, then ...This paper presents a new method exactly to solve the bending of elastic thinplates with arbitrary shape. First the analytic solution of differential equation ofelastic thin plate is derived in polar coordinate, then the analytic solution is substituted into the boundary conditions of elastic thin plate with arbitrary shape. The boundaryequations are expanded along the boundary by the use of Fourier series, all unknown coefficients can be decided. The results are exact.展开更多
Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordi...Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.展开更多
The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtra...The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration and consequently has got, through various forms of limits, the exact analytical solutions of the three common reservoirs (fissure, homogeneous and the two-layered) pressure distribution under the conditions of three boundaries, i.e., infinite boundary, sealed finite boundary and the finite boundary at constant pressures.展开更多
An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are relate...An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.展开更多
By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we ...By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.展开更多
The modified Emden-type is being investigated by mathematicians as well as physicists for about a century. However, there exist no exact explicit solution of this equation, ẍ+ αxẋ+ βx3 = 0 for ar...The modified Emden-type is being investigated by mathematicians as well as physicists for about a century. However, there exist no exact explicit solution of this equation, ẍ+ αxẋ+ βx3 = 0 for arbitrary values of α and β. In this work, the exact analytical explicit solution of modified Emden-type (MEE) equation is derived for arbitrary values of α and β. The Lagrangian and Hamiltonian of MEE are also worked out. The solution is also utilized to find exact explicit analytical solution of Force-free Duffing oscillator-type equation. And exact explicit analytical solution of two-dimensional Lotka-Volterra System is also worked out.展开更多
基金This workis supported by the National Natural Science Foundation of China under Grant (60372095)by the science and technology development pro-gramof Beijing Municipal Commission of Education (KM200410772002)by the Beijing Excellent Talent Fund.
文摘The Caudrey-Dodd-Gibbon-Kotera Sawada (CDGKS) equation has attracted many physicists and mathematicians. In this paper, based on the idea of variable-coefficient balancing-act method and the computerized .symbolic compu tation, some exact analytic solutions for the CDGKS equation have been obtained.
基金supported by the National Natural Science Foundation of China(11102237)Program for Changjiang Scholars and Innovative Research Team in University(IRT1294)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20110133120012)China Scholarship Council(CSC)
文摘Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.
文摘This paper presents a new method exactly to solve the bending of elastic thinplates with arbitrary shape. First the analytic solution of differential equation ofelastic thin plate is derived in polar coordinate, then the analytic solution is substituted into the boundary conditions of elastic thin plate with arbitrary shape. The boundaryequations are expanded along the boundary by the use of Fourier series, all unknown coefficients can be decided. The results are exact.
文摘Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.
文摘The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration and consequently has got, through various forms of limits, the exact analytical solutions of the three common reservoirs (fissure, homogeneous and the two-layered) pressure distribution under the conditions of three boundaries, i.e., infinite boundary, sealed finite boundary and the finite boundary at constant pressures.
基金Project supported by the Shahrood University of Technology (No. 17024),Iran
文摘An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.
基金Project supported in part by the Natural Science Foundation of China (Grant Nos. 10575040,90503010,10634060 and 10874050)by National Basic Research Program of China (Grant No. 2005CB724508)+1 种基金the Foundation from the ministry of the National Education of China (Grant No. 200804870051)the Science Innovation Foundation of Huazhong University of Science and Technology (Grant No. HF-06-010-08-012)
文摘By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.
文摘The modified Emden-type is being investigated by mathematicians as well as physicists for about a century. However, there exist no exact explicit solution of this equation, ẍ+ αxẋ+ βx3 = 0 for arbitrary values of α and β. In this work, the exact analytical explicit solution of modified Emden-type (MEE) equation is derived for arbitrary values of α and β. The Lagrangian and Hamiltonian of MEE are also worked out. The solution is also utilized to find exact explicit analytical solution of Force-free Duffing oscillator-type equation. And exact explicit analytical solution of two-dimensional Lotka-Volterra System is also worked out.
