Nonlocal symmetries and interaction solutions for the KdV-type equation

Peer review under responsibility of University of Bahrain.

Abstract

The nonlocal symmetries for the special equation, which is called KdV-type equation, are obtained by means of the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables and the corresponding finite symmetry transformations are computed directly. The KdV-type equation is also proved to be consistent tanh expansion solvable. New exact interaction excitations such as soliton–cnoidal wave solutions are given out analytically and graphically.

Keywords:

• Nonlocal symmetries
• Consistent tanh expansion
• Soliton-cnoidal wave solutions

Acknowledgements

The work is supported by National Natural Science Foundation of China (Nos. 11071164 and 11201302), Shanghai Natural Science Foundation (No. 10ZR1420800), the Hujiang Foundation of China (B14005).

Notes

Peer review under responsibility of University of Bahrain.