The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explic...The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.展开更多
A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomt...A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev–Petviashvili equation, some B¨acklund transformations(BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further,by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev–Petviashvili equation is proved consistent Riccati expansion(CRE)solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.11505154the Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ16A010003the Scientific Research Foundation for Doctoral Program of Zhejiang Ocean University under Grant No.Q1511
文摘The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of under Grant Nos.11275072 and 11435005+3 种基金Doctoral Program of Higher Education of China under Grant No.20120076110024the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213Zhejiang Provincial Natural Science Foundation of China under Grant No.LY14A010005
文摘A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev–Petviashvili equation, some B¨acklund transformations(BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further,by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev–Petviashvili equation is proved consistent Riccati expansion(CRE)solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.
