Non-Lie Symmetry Groups and New Exact Solutions to the (2 + 1)-Dimensional Broer-Kaup System


For the (2 + 1)-dimensional Broer-Kaup system, we study the corresponding Lie symmetry groups, and obtain the symmetry group theorem and the Backlund transformation formula of solutions finding. At the same time, we find some new exact solutions of the (2 + 1)-dimensional Broer-Kaup system and extend the results in the papers [1-4].

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B. Zheng and X. Liu, "Non-Lie Symmetry Groups and New Exact Solutions to the (2 + 1)-Dimensional Broer-Kaup System," Advances in Pure Mathematics, Vol. 3 No. 1, 2013, pp. 149-152. doi: 10.4236/apm.2013.31020.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. F. Zhang and P. Han, “The Regional Structure of (2 + 1)-Dimensional Broer-Kaup Equation,” Physics Journal, Vol. 51, 2002, pp. 705-711.
[2] X. Q. Liu, “New Explicit Solutions to the 2 + 1 Dimensional Broer-Kaup Equations,” Journal of Partial Differential Equations, Vol. 17, 2004, pp. 1-11.
[3] C. L. Bai, X. Q. Liu, C. J. Bai and B. Z. Xu, “Multiple Soliton Solutions of the 2 + 1 Dimensional Broer-Kaup Equations,” Acta Photonica Sinica, Vol. 28, 1999, pp. 1029-1031.
[4] C. L. Bai, X. Q. Liu and H. Zhao, “New Localized Excitations in a (2 + 1) Dimensional Broer-Kaup System,” Chinese Physics, Vol. 14, No. 2, 2005, pp. 285-292. doi:10.1088/1009-1963/14/2/012
[5] S. Y. Lou and X. B. Hu, “Broer-Kaup System from Dar Boux Transformation Related Symmetry Constraints of Kadomtsev-Petviashvili Equation,” Communications in Theoretical Physics, Vol. 29, No. 1, 1998, pp. 145-148.
[6] H. Y. Ruan and Y. X. Chen, ActaPhys.Sin. (Over. Ed.), Vol. 7, 1998, 241.
[7] D. J. Huang and H. Q. Zhang, “Variable Coefficient Projective Riccati Equation Method and Its Application to a New 2 + 1 Dimensional Simplified Generalized Broer-Kaup System,” Chaos, Solitons and Fractals, Vol. 23, No. 2, 2005, pp. 601-607. doi:10.1016/j.chaos.2004.05.011
[8] P. J. Olver, “Applications of Lie Groups to Differential Equations,” Springer-Verlag, New York, 1993. doi:10.1007/978-1-4612-4350-2
[9] P. A. Clarkson, “Nonclassical Symmetry Reduction of the Boussinesq Equation,” Chaos, Solitons and Fractals, Vol. 5, No. 12, 1995, pp. 2261-2301. doi:10.1016/0960-0779(94)E0099-B
[10] P. A. Clarkson and M. D. Kruskal, “New Similarity Solutions of the Boussinesq Equation,” Journal of Mathematical Physics, Vol. 30, No. 10, 1989, pp. 2201-2213. doi:10.1063/1.528613
[11] S. Y. Lou and H. C. Ma, “Non-Lie Symmetry Groups of 2 + 1 Dimensional Nonlinear Systems Obtained from a Simple Direct Method,” Journal of Physics A: Mathematical and General, Vol. 38, No. 7, 2005, pp. L129-137. doi:10.1088/0305-4470/38/7/L04
[12] H. C. Ma, “A Simple Method to General Lie Point Symmetry Groups of the 3 + 1 Dimensional Jimbo-Miwa Equation,” Chinese Physics Letters, Vol. 22, No. 3, 2005, pp. 554-557. doi:10.1088/0256-307X/22/3/010

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