The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time-...The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.展开更多
In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new ...In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.展开更多
基金The project supported by the National Fundamental Research Program of China(973 Program)under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028
文摘The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.
文摘In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.
