Exact periodic, cusp, solitary and loop wave solutions of the EX-ROE

Abstract

The extended reduced Ostrovsky equation (EX-ROE) is investigated by using the dynamical system theory. The bifurcation phase portraits are drawn in different regions of parameter plane. The bounded travelling wave solutions such as periodic waves, periodic cusp waves, solitary waves, peakon, solitary loop waves and periodic loop waves are obtained. The dynamic characters of these solutions are investigated.

Keywords:

• extended reduced Ostrovsky equation
• periodic wave
• solitary wave
• solitary loop wave
• periodic loop wave

2000 AMS Subject Classifications :

• 35Q51
• 35Q58
• 37K50

Acknowledgements

The authors sincerely thank the referee for his/her many valuable comments which helped us improve the paper. This work was supported by the Natural Science Foundation of China (No.10871073) and Yunnan Province (2008ZC153M).