By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given...By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.展开更多
In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of t...In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of the extended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutions of these veKP equations can be constructed via the simple veKP equations or constant-coefficient KP equations.展开更多
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parame...The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.展开更多
Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differentia...Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.展开更多
In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein conden...In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.展开更多
In the paper, a generalized sub-equation method is presented to construct some exact analytical solutions of nonlinear partial differential equations. Making use of the method, we present rich exact analytical solutio...In the paper, a generalized sub-equation method is presented to construct some exact analytical solutions of nonlinear partial differential equations. Making use of the method, we present rich exact analytical solutions of the onedimensional nonlinear Schrfdinger equation which describes the dynamics of solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential. The solutions obtained include not only non-traveling wave and coefficient function＇s soliton solutions, but also Jacobi elliptic function solutions and Weierstra.ss elliptic function solutions. Some plots are given to demonstrate the properties of some exact solutions under the Feshbachmanaged nonlinear coefficient and the hyperbolic secant function coefficient.展开更多
On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensiona...On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensional partial differential equations.We focus on solving the third type of reduction and dividing them into threesubcases,from which we obtain rich solutions including some arbitrary functions.展开更多
基金Supported by the Natural Science Foundation of China under Grant No. 10735030Ningbo Natural Science Foundation under Grant No. 2008A610017+3 种基金National Basic Research Program of China (973 Program 2007CB814800)Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C. Wong Magna Fund in Ningbo University
文摘By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.
基金Supported by the National Natural Science Foundation of China under Grant No. 0735030Zhejiang Provincial Natural Science Foundations of China under Grant No. Y6090592+1 种基金National Basic Research Program of China (973 Program 2007CB814800)Ningbo Natural Science Foundation under Grant No. 2008A610017 and K.C. Wong Magna Fund in Ningbo University
文摘In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of the extended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutions of these veKP equations can be constructed via the simple veKP equations or constant-coefficient KP equations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10735030)National Basic Research Program of China (Grant No. 2007CB814800)+1 种基金Ningbo Natural Science Foundation (Grant No. 2008A610017)K.C. Wong Magna Fund in Ningbo University
文摘The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.
基金Supported by K.C. Wong Magna Fund in Ningbo University, NSF of China under Grant Nos. 10747141 and 10735030Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408the Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093
文摘Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.
基金The project supported by Natural Science Foundation of Zhejiang Province of China under Grant Nos. Y604056 and 605408 and the Doctoral Foundation of Ningbo City under Grant No, 2005A61030
文摘In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant Nos. 605408 and Y604056, the Doctoral Foundation of Ningbo City under Grant No. 2005A61030, and the Postdoctoral Science Foundation of China under Grant No. 2005038441
文摘In the paper, a generalized sub-equation method is presented to construct some exact analytical solutions of nonlinear partial differential equations. Making use of the method, we present rich exact analytical solutions of the onedimensional nonlinear Schrfdinger equation which describes the dynamics of solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential. The solutions obtained include not only non-traveling wave and coefficient function＇s soliton solutions, but also Jacobi elliptic function solutions and Weierstra.ss elliptic function solutions. Some plots are given to demonstrate the properties of some exact solutions under the Feshbachmanaged nonlinear coefficient and the hyperbolic secant function coefficient.
基金supported by National Natural Science Foundation of China under Grant Nos.10735030 and 90718141Shanghai Leading Academic Discipline Project under Grant No.B412+3 种基金Natural Science Foundations of Zhejiang Province of China under Grant No.Y604056Doctoral Foundation of Ningbo City under Grant No.2005A61030Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0734K.C.Wang Magna Fund in Ningbo University
文摘On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensional partial differential equations.We focus on solving the third type of reduction and dividing them into threesubcases,from which we obtain rich solutions including some arbitrary functions.
