In this paper,a Boussinesq hierarchy in the bilinear form is proposed. A Backlund transformation for this hierarchy is presented and the nonlinear superposition formula is proved rigorously.
In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applicati...In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten-Krasil'shchik coupled KdV-mKdV system.展开更多
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tan...To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-Sivashinsky equation and the set of （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.展开更多
In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present...In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present infinite sequence solutions for space-time fractional symmetric regularized long wave equation. This method can be extended to solve other nonlinear fractional partial differential equations.展开更多
A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋...A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋1）- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this （1＋1）-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.展开更多
文摘In this paper,a Boussinesq hierarchy in the bilinear form is proposed. A Backlund transformation for this hierarchy is presented and the nonlinear superposition formula is proved rigorously.
基金supported by the National Natural Science Foundation of China (Grant Nos.12175111,11931107 and 12171474)NSFC-RFBR (Grant No.12111530003)。
文摘In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten-Krasil'shchik coupled KdV-mKdV system.
基金Project supported by the National Natural Science Foundation of China(Grant No.10461006)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)+1 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.200408020103)the Natural Science Research Program of Inner Mongolia Normal University,China(Grant No.QN005023)
文摘To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-Sivashinsky equation and the set of （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
基金Acknowledgments This work is supported by the National Natural Science Foundation of China （Grant No. 11462019） and the Scientific Research Foundation of Inner Mongolia University for Nationalities （Grant No. NMD1306）. The author would like to thank the referees for their time and comments.
文摘In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present infinite sequence solutions for space-time fractional symmetric regularized long wave equation. This method can be extended to solve other nonlinear fractional partial differential equations.
文摘A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋1）- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this （1＋1）-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.
