Nonlinear Dynamics

, Volume 92, Issue 2, pp 235–246

# On the integrability and Riemann theta functions periodic wave solutions of the Benjamin Ono equation

• Chun-Mei Fang
• Shou-Fu Tian
• Yang Feng
• Jin-Hua Dai
Original Paper

## Abstract

In this paper, the complete integrability of the Benjamin Ono equation is systematically studied. Its bilinear equation, soliton solutions, bilinear Bäcklund transformation and Lax pair are successfully obtained, by virtue of generalized Bell’s polynomials scheme. Moreover, by using multidimensional Riemann theta functions, the periodic wave solutions of the Benjamin Ono equation are constructed. Further, the asymptotic behaviors of the periodic wave solutions are presented with a limiting procedure, which shows the relations between the periodic wave solutions and soliton solutions.

## Keywords

The Benjamin Ono equation Bell’s polynomials Bäcklund transformation Lax pair Periodic wave solution

## Notes

### Acknowledgements

This work is supported by the Fundamental Research Fund for the Central Universities under the Grant No. 2017XKQY101.

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## Authors and Affiliations

• Chun-Mei Fang
• 1
• Shou-Fu Tian
• 2
• Yang Feng
• 3
• Jin-Hua Dai
• 1
1. 1.School of MathematicsJining Normal UniversityWulanchabuPeople’s Republic of China
2. 2.School of MathematicsChina University of Mining and TechnologyXuzhouPeople’s Republic of China
3. 3.School of ScienceXi’an University of Post and TelecommunicationsXi’anPeople’s Republic of China