The bilinear equation of the genera/nonlinear Schrodinger equation with derivative (GDNLSE) and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively....The bilinear equation of the genera/nonlinear Schrodinger equation with derivative (GDNLSE) and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative (DNLSE) and its multisoliton solutions are given by reduction.展开更多
To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the tim...To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.展开更多
The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.
In this paper,dependent and independent variable transformations are introduced to solve the negativemKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions.It is shown...In this paper,dependent and independent variable transformations are introduced to solve the negativemKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions.It is shownthat different kinds of solutions can be obtained to the negative mKdV equation,including breather lattice solution andperiodic wave solution.展开更多
The solution transformations and properties of the -matrices for two-component systems under these transformations are analyzed in details. Not all transformed -matrices can be put into the Skalyanin's formalism. ...The solution transformations and properties of the -matrices for two-component systems under these transformations are analyzed in details. Not all transformed -matrices can be put into the Skalyanin's formalism. For those -matrices with all required properties, the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed. These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation, or its coupling coefficients are multiplied by an overall factor, or the spin of the system is rotated around the axis or/and reflected with respect to some plane. In these cases, the transformed systems remain to be integrable.展开更多
For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,...For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.展开更多
By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution i...By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the (N - 1)- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.展开更多
The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier trans...The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.展开更多
Based on the method developed by Nucci, the pseudopotentials, Lax pairs and the mngulanty mamtoia equations of the generalized fifth-order KdV equation are derived. By choosing different coefficient, the corresponding...Based on the method developed by Nucci, the pseudopotentials, Lax pairs and the mngulanty mamtoia equations of the generalized fifth-order KdV equation are derived. By choosing different coefficient, the corresponding results and the Backlund transformations can be obtained on three conditioners which include Caudrey-Dodd-Cibbon- Sawada-Kotera equation, the Lax equation and the Kaup-kupershmidt equation.展开更多
An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad cal...An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation (Eq. (23)) is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained (Eq. (36)) after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. (36) are closer to the Fourier model. The convex nature of the temperature curve is present.展开更多
Hierarchically nanostructured, porous TiO_2(B) microspheres were synthesized by a microwave-assisted solvothermal method combined with subsequent heat treatment in air. The materials were carefully characterized by sc...Hierarchically nanostructured, porous TiO_2(B) microspheres were synthesized by a microwave-assisted solvothermal method combined with subsequent heat treatment in air. The materials were carefully characterized by scanning and transmission electron microscopy, X-ray diffraction, CO_2 adsorption, and a range of spectroscopies, including Raman, infrared, X-ray photoelectron and UV-Vis spectroscopy. The hierarchical TiO_2(B) particles are constructed by ultrathin nanosheets and possess large specific surface area, which provided many active sites for CO_2 adsorption as well as CO_2 conversion. The TiO_2(B)nanostructures exhibited marked photocatalytic activity for CO_2 reduction to methane and methanol. Anatase TiO_2 and P25 were used as the reference photocatalysts. Transient photocurrent measurement also proved the higher photoactivity of TiO_2(B) than that of anatase TiO_2. In-situ infrared spectrum was measured to identify the intermediates and deduce the conversion process of CO_2 under illumination over TiO_2(B) photocatalyst.展开更多
Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. The...Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are stud- ied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations.展开更多
In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like ...In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like extremal surfaces can be described by a system Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10671121
文摘The bilinear equation of the genera/nonlinear Schrodinger equation with derivative (GDNLSE) and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative (DNLSE) and its multisoliton solutions are given by reduction.
文摘To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.
基金National Natural Science Foundation of China under Grant Nos.10871165 and 10671121
文摘The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.
基金Supported by National Natural Science Foundation of China under Grant No.90511009National Basic Research Program of China under Grant Nos.2006CB403600 and 2005CB42204
文摘In this paper,dependent and independent variable transformations are introduced to solve the negativemKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions.It is shownthat different kinds of solutions can be obtained to the negative mKdV equation,including breather lattice solution andperiodic wave solution.
基金Natural Science Foundation of Science and Technology Committee of Henan Proviuce,河南师范大学校科研和教改项目
文摘The solution transformations and properties of the -matrices for two-component systems under these transformations are analyzed in details. Not all transformed -matrices can be put into the Skalyanin's formalism. For those -matrices with all required properties, the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed. These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation, or its coupling coefficients are multiplied by an overall factor, or the spin of the system is rotated around the axis or/and reflected with respect to some plane. In these cases, the transformed systems remain to be integrable.
基金国家自然科学基金,湖南省自然科学基金,the Scientific Research Foundation of Education Burean of Hunan Province
文摘For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.
基金supported by National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Key Project of the Ministry of Education under Grant No.106033+2 种基金the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,the National Basic Research Program of China(973 Program)under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024,the Ministry of Education
文摘By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the (N - 1)- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.
基金Supported by the National Natural Science Foundation of China Grant No.10874098the National Basic Research Program of China under Grant Nos.2009CB929402 and 2011CB9216002
文摘The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030,11075055,and 90718041the Shanghai Leading Academic Discipline Project,China under Grant No.B412+1 种基金the Program for Changjiang Scholars,the Innovative Research Team in University of Ministry of Education of China under Grant No.IRT 0734the K.C.Wong Magna Fund in Ningbo University
文摘Based on the method developed by Nucci, the pseudopotentials, Lax pairs and the mngulanty mamtoia equations of the generalized fifth-order KdV equation are derived. By choosing different coefficient, the corresponding results and the Backlund transformations can be obtained on three conditioners which include Caudrey-Dodd-Cibbon- Sawada-Kotera equation, the Lax equation and the Kaup-kupershmidt equation.
文摘An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation (Eq. (23)) is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained (Eq. (36)) after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. (36) are closer to the Fourier model. The convex nature of the temperature curve is present.
基金supported by the National Basic Research Program of China(2013CB632402)the National Natural Science Foundation of China(51320105001,21433007,51372190,21573170)+3 种基金the Natural Science Foundation of Hubei Province(2015CFA001)the Fundamental Research Funds for the Central Universities(WUT:2015-III-034)Innovative Research Funds of SKLWUT(2017-ZD-4)the Discovery Early Career Researcher Award(DECRA)by Australian Research Council(DE160101488)
文摘Hierarchically nanostructured, porous TiO_2(B) microspheres were synthesized by a microwave-assisted solvothermal method combined with subsequent heat treatment in air. The materials were carefully characterized by scanning and transmission electron microscopy, X-ray diffraction, CO_2 adsorption, and a range of spectroscopies, including Raman, infrared, X-ray photoelectron and UV-Vis spectroscopy. The hierarchical TiO_2(B) particles are constructed by ultrathin nanosheets and possess large specific surface area, which provided many active sites for CO_2 adsorption as well as CO_2 conversion. The TiO_2(B)nanostructures exhibited marked photocatalytic activity for CO_2 reduction to methane and methanol. Anatase TiO_2 and P25 were used as the reference photocatalysts. Transient photocurrent measurement also proved the higher photoactivity of TiO_2(B) than that of anatase TiO_2. In-situ infrared spectrum was measured to identify the intermediates and deduce the conversion process of CO_2 under illumination over TiO_2(B) photocatalyst.
基金Supported by National Natural Science Foundation of China under Grant No.11271168the Priority Academic Program Development of Jiangsu Higher Education InstitutionsInnovation Project of the Graduate Students in Jiangsu Normal University
文摘Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are stud- ied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations.
基金Supported by National Natural Science Foundation of China under Grant Nos.11026151,11101001the Anhui Provincial University’s Natural Science Foundation under Grant No.KJ2010A130
文摘In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like extremal surfaces can be described by a system Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.