Nonlinear Dynamics

, Volume 88, Issue 4, pp 2503–2511 | Cite as

Optimal system, group invariant solutions and conservation laws of the CGKP equation

  • Lihua Zhang
  • Fengsheng Xu
  • Lixin Ma
Original Paper


In this paper, the (2 + 1)-dimensional cubic generalized Kadomtsev–Petviashvili (CGKP) equation that is derived from the Maxwell–Bloch equations is investigated. By means of Lie symmetry analysis method, we obtain the Lie point symmetries for the equation and the optimal system of the symmetry algebra. Based on the optimal system, a lot of group invariant solutions are obtained. In addition, explicit conservation laws of the equation are studied.


CGKP equation Symmetries Optimal system Group invariant solutions Conservation laws 



The work is supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2013AQ005) and National Natural Science Foundation of China (Grant No. 11501082).


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsDezhou UniversityDezhouPeople’s Republic of China

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