Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev Petviashvili Equation

作者：Huang, Li-Li; Chen, Yong^*; Ma, Zheng-Yi

来源：Communications in Theoretical Physics, 2016, 66(2): 189-195.

DOI：10.1088/0253-6102/66/2/189

• nonlocal symmetry
• consistent riccati expansion
• Painleve expansion
• soliton-cnoidal wave solution

A generalized Kadomtsev-Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painleve analysis to the generalized Kadomtsev Petviashvili equation, some Backlund 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 Painleve 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.

• 出版日期2016-8-1
• 单位丽水学院; 华东师范大学