The Solitary Waves Solutions of the Internal Wave Benjamin-Ono Equation


The Benjamin-ono (BO) equation is an important nonlinear wave model which can describe the deep oceanic internal wave propagation. In this paper, the multi-algebraic solitary wave solutions for the internal wave BO equation including the linear velocity term in matrix form are given by the bilinear form. Based on the analytic solutions of the BO equation obtained in this paper and considering the hydrological parameters, the propagation of one-solitary wave and different kinds of interaction for the two-solitary waves are discussed and illustrated.

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Meng, X. (2014) The Solitary Waves Solutions of the Internal Wave Benjamin-Ono Equation. Journal of Applied Mathematics and Physics, 2, 807-812. doi: 10.4236/jamp.2014.28089.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, New York.
[2] Jackson, C. (2007) Internal Wave Detection Using the Moderate Resolution Imaging Spectroradiometer (MODIS). Journal of Geophysical Research, 112, Article ID: C11012.
[3] Zheng, Y., Xin, D.Q., Li, S.X., Shi, G.Q., Wei, J.X., Wei, X. and Duan, Y.N. (2013) Current Field Features and Propagation Characteristics of Suspected Internal Solitary Wave Packet. Ocean Engineering, 72, 448-452.
[4] Zheng, Q.N., Klemas, V. and Yan, X.H. (1995) Dynamic Interpretation of Space Shuttle Photographs: Deep Water Internal Waves in the Western Equatorial Indian Ocean. Journal of Geophysical Research, 100, 2579-2589.
[5] Djordjevic, V.D. and Redekopp, L.G. (1978) The Fission and Disintegration of Internal Solitary Waves Moving over Two-Dimensional Topography. Journal of Physical Oceanography, 8, 1016-1024.<1016:TFADOI>2.0.CO;2
[6] Ostrosky, L.A. and Stepanyants, Y.A. (1989) Do Internal Solitons Exist in the Ocean? Reviews of Geophysics, 27, 293-310.
[7] Grimshaw, R., Pelinovsky, E. and Talipova T. (1997) The Modified Korteweg-de Vries Equation in the Theory of Large-Amplitude Internal Waves. Nonlinear Processes in Geophysics, 4, 237-250.
[8] Liu, A.K., Holbrook, J.R. and Apel, J.R. (1985) Nonlinear Internal Wave Evolution in the Sulu Sea. Journal of Physical Oceanography, 15, 1613-1624.<1613:NIWEIT>2.0.CO;2
[9] Joseph, R.I. (1977) Solitary Waves in a Finite Depth Fluid. Journal of Physics A, 10, 225-227.
[10] Benjamin, T.B. (1967) Internal Waves of Permanent form in Fluids of Great Depth. Journal of Fluid Mechanics, 29, 559-592.
[11] Davis, R.E. and Acrivost, A. (1967) Solitary Internal Waves in Deep Water. Journal of Fluid Mechanics, 29, 593-608.
[12] Ono, H. (1979) Algebraic Solitary Waves in Stratified Fluids. Journal of the Physical Society of Japan, 39, 1082-1091.
[13] Luo, D.H. (1989) On the Benjamin-Ono Equation and Its Generalization in the Atmosphere. Science in China (Seris B), 32, 1233-1245.
[14] Matsuno, Y. (1979) Exact Multi-Soliton Solution of the Benjamin-Ono Equation. Journal of Physics A, 12, 619-621.
[15] Nakamura, A. (1979) Backlund Transform and Conservation Laws of the Benjamin-Ono Equation. Journal of the Physical Society of Japan, 47, 1335-1340.
[16] Meiss, J.D. and Perreira, N.R. (1978) Internal Wave Solitons. Physics of Fluids, 21, 700-702.
[17] Hu, X.B. (1994) Nonlinear Superposition Formula of the Novikov-Veselov Equation. Journal of Physics A, 27, 1331-1338.
[18] Ma, W.X., Wu, H.Y. and He, J.S. (2007) Partial Differential Equations Possessing Frobenius Integrable Decomposi-tions. Physics Letters A, 364, 29-32.
[19] Meng, X.H., Tian, B., Xu, T., Zhang, H.Q. and Feng, Q. (2009) Solitonic Solutions and Backlund Transformation for the Inhomogeneous N-Coupled Nonlinear Schrodinger Equations. Physica A, 388, 209-217.
[20] Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press, Cambridge.

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