摘要
The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev′e method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems.The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion(CTE) method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.
The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev6 method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems. The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion （CTE） method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.
基金
Supported by the National Natural Science Foundation of China under Grant Nos.11305106,11405110,11305031,and 11275129
the Natural Science Foundation of Zhejiang Province of China under Grant No.LQ13A050001
the Natural Science Foundation of Guangdong Province under Grant No.S2013010011546
