On the integrability and Riemann theta functions periodic wave solutions of the Benjamin Ono equation |
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| Authors: | Chun-Mei Fang Shou-Fu Tian Yang Feng Jin-Hua Dai |
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| Institution: | 1.School of Mathematics,Jining Normal University,Wulanchabu,People’s Republic of China;2.School of Mathematics,China University of Mining and Technology,Xuzhou,People’s Republic of China;3.School of Science,Xi’an University of Post and Telecommunications,Xi’an,People’s Republic of China |
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| 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. |
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