In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
A new method for constructing the Wronskian entries is proposed and applied to the differential-difference Kadomtsev-Petviashvilli （DΔKP） equation. The generalized Wronskian solutions to it are obtained, including ...A new method for constructing the Wronskian entries is proposed and applied to the differential-difference Kadomtsev-Petviashvilli （DΔKP） equation. The generalized Wronskian solutions to it are obtained, including rational solutions and Matveev solutions.展开更多
By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two ...By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves.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
Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial d...Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.展开更多
The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian form...The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian formulation is constructed by employing the Wronskian conditions of the KdV equation. Applications are made for the （3＋1）- dimensional generalized KP, BKP and Jimbo-Miwa equations, thereby presenting their Wronskian sufficient conditions. An N-soliton solution in terms of Wronskian determinant is obtained. Under a dimensional reduction, our results yield Wronskian solutions of the KdV equation.展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10371070 and 10671121 .Acknowledgments The authors exPress their thanks to Prof. D.J. Zhang and Dr. J.B. Bi for their good advices.
文摘A new method for constructing the Wronskian entries is proposed and applied to the differential-difference Kadomtsev-Petviashvilli （DΔKP） equation. The generalized Wronskian solutions to it are obtained, including rational solutions and Matveev solutions.
文摘By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves.
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Supported by the National Natural Science Foundation of China under Grant No.11171312
文摘Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.
基金Supported by the National Natural Science Foundation of China under Grant No.11371326
文摘The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian formulation is constructed by employing the Wronskian conditions of the KdV equation. Applications are made for the （3＋1）- dimensional generalized KP, BKP and Jimbo-Miwa equations, thereby presenting their Wronskian sufficient conditions. An N-soliton solution in terms of Wronskian determinant is obtained. Under a dimensional reduction, our results yield Wronskian solutions of the KdV equation.
