References
- M.S. Ismail and A. Biswas,1-Soliton solution of the generalized KdV equation with generalized evolution, Appl. Math. Comp. 216 (2010), 1673-1679. https://doi.org/10.1016/j.amc.2010.02.045
- A.M. Wazwaz, New sets of solitary wave solutions to the KdV, mKdV and generalized KdV equations, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 331-339. https://doi.org/10.1016/j.cnsns.2006.03.013
- T. Xiao-Yan, H. Fei and L. Sen-Yue, Variable coefficient KdV equation and the analytic diagnosis of a pole blocking life cycle, Chinese Phys. Lett. 23 (2006), 887-890. https://doi.org/10.1088/0256-307X/23/4/035
- A.G. Johnpillai, C.M. Khalique and Anjan Biswas, Exact solutions of KdV equation with time-dependent coefficients, Appl. Math. Comp. 216 (2010), 3114-3119. https://doi.org/10.1016/j.amc.2010.03.133
- A.M.Wazwaz, Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method, Appl. Math. Comput. 182 (2006), 283-300. https://doi.org/10.1016/j.amc.2006.02.047
- A. Biswas,Solitary wave solution for the generalized KdV equation with time-dependent damping and dispersion, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 3503-3506. https://doi.org/10.1016/j.cnsns.2008.09.026
- A.G. Johnpillai and C.M. Khalique,Group analysis of KdV equation with time dependent coefficients, Appl. Math. Comput. 216 (2010), 3761-3771. https://doi.org/10.1016/j.amc.2010.05.043
- A.G. Johnpillai and C.M. Khalique, Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1207-1215. https://doi.org/10.1016/j.cnsns.2010.06.025
- H. Liu, J. Li and L. Liu, Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations, J. Math. Anal. Appl. 368 (2010), 551-558. https://doi.org/10.1016/j.jmaa.2010.03.026
- W. Chen, J. Li, C. Miao and J. Wu, Low regularity solutions of two fifth-order KdV type equations, J. Anal. Math. 107 (2009), 221-238. https://doi.org/10.1007/s11854-009-0009-0
- P.J. Olver, Application of Lie Group to Differential Equation, Springer,New York,1986.
- L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.
- S. Lie, On integration of a class of linear partial differential equations by means of definite integrals, Arch. Math. VI (3) (1881), 328-368.
- G.W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York,1989.
- N.H. Ibragimov (Ed.), CRC Handbook of Lie Group Analysis of Differential Equations, Vols. 1-3, CRC Press, Boca Raton, FL., 1994.
- Z.L. Yan and X.Q. Liu, Symmetry and similarity solutions of variable coefficients generalized Zakharov-Kuznetsov equation, Appl. Math. Comput. 180 (2006), 288-294. https://doi.org/10.1016/j.amc.2005.12.021
- N. Liu and X.Q. Liu, Similarity reductions and similarity solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation, Chin. Phys. Lett. 25 (2008), 3527-3530. https://doi.org/10.1088/0256-307X/25/10/003
- B. Xu and X.Q. Liu, Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation, Appl. Math. Comput. 215 (2009), 1244-1250. https://doi.org/10.1016/j.amc.2009.06.062
- J.Q. Yu, X.Q. Liu and T.T. Wang, Exact solutions and conservation laws of (2+1)-dimensional Boiti-Leon-Pempinelli equation, Appl. Math. Comput. 216 (2010), 2293-2300. https://doi.org/10.1016/j.amc.2010.03.065
- M.S., D.P. and B.M.V., New exact explicit solutions of the generalized KdV equations, Appl. Math. Comput. 202 (2008), 693-699. https://doi.org/10.1016/j.amc.2008.03.013
- H. Liu and J. Li. Lie symmetry analysis and exact solutions for the short pulse equation, Nonlinear Anal. 71 (2009), 2126-2133. https://doi.org/10.1016/j.na.2009.01.075
Cited by
- Group analysis of variable coefficient generalized fifth-order KdV equations vol.11, pp.7, 2014, https://doi.org/10.1134/S1547477114070280