In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobi...In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.展开更多
In this paper, using the generalized （G1/G）-expansion method and the auxiliary differential equation method, we discuss the （2＋1）-dimensional canonical generalized KP （CGKP）, KdV, and （2＋1）-dimensional Burge...In this paper, using the generalized （G1/G）-expansion method and the auxiliary differential equation method, we discuss the （2＋1）-dimensional canonical generalized KP （CGKP）, KdV, and （2＋1）-dimensional Burgers equations with variable coetticients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions.展开更多
For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In add...For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.展开更多
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y605312.
文摘In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.
基金Supported by the Natural Science Foundation of Shandong Province under Grant Nos.Q2005A01 and Y2007G64
文摘In this paper, using the generalized （G1/G）-expansion method and the auxiliary differential equation method, we discuss the （2＋1）-dimensional canonical generalized KP （CGKP）, KdV, and （2＋1）-dimensional Burgers equations with variable coetticients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y6090131the Natural Science Foundation of Ningbo City under Grant No.2010A610101
文摘For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.
