The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the...The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the bilinear Backlund transformation from its Lax pairs and find solutions with the help of the obtained bilinear Bgcklund transformation.展开更多
N-soliton solutions in the Wronskian form for the KdV equation with loss and nonuniformity terms were obtained. New rational-like solutions and mixed solutions were further derived. All these solutions were verified b...N-soliton solutions in the Wronskian form for the KdV equation with loss and nonuniformity terms were obtained. New rational-like solutions and mixed solutions were further derived. All these solutions were verified by direct substitutions into bilinear equation.展开更多
Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by th...Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between （N-1）- soliton-like and N-soliton-like solutions is verified.展开更多
By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Singl...By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10371070, and the Postdoctoral Science Foundation of China.
文摘The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the bilinear Backlund transformation from its Lax pairs and find solutions with the help of the obtained bilinear Bgcklund transformation.
文摘N-soliton solutions in the Wronskian form for the KdV equation with loss and nonuniformity terms were obtained. New rational-like solutions and mixed solutions were further derived. All these solutions were verified by direct substitutions into bilinear equation.
基金Supported by the Key Project of the Ministry of Education of China under Grant No 106033, and the National Natural Science Foundation of China under Grant Nos 60372095 and 10272017, the Green Path Programme of Air Force of the Chinese People＇s Liberation Army, the Cheung Kong Scholars Programme of the Ministry of Education of China, and Li Ka Shing Foundation of Hong Kong.
文摘Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between （N-1）- soliton-like and N-soliton-like solutions is verified.
基金Science and Engineering Research Board(DST,Govt.of India)Grant No.SR/FTP/MS-020/2011Chinese Academy of Sciences President’s International Fellowship Initiative,Grant No.2015PM034。
文摘By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.
