Abstract
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.
Highlights
Since the solitary wave was discovered in 1834, the researches on the nonlinear solitary wave propagation phenomena have been widely developed [1]
The internal solitary wave (ISW) is the nonlinear large amplitude wave existing in the ocean pycnocline
The ISWs have been observed by the synthetic aperture radar and on-site measurement in several ocean areas [2]
Summary
Since the solitary wave was discovered in 1834, the researches on the nonlinear solitary wave propagation phenomena have been widely developed [1]. The BO equation is an integro-differential type equation which can describe the internal wave propagation in a deep stratified fluid [10]-[12]. It can describe the mesoscale motion in the atmosphere if the meridional disturbance wind is weak [13]. There are many analytical methods for solving the nonlinear differential equations, among which the bilinear method is one direct and efficient way for obtaining the multi-solitary wave solutions [17]-[19]. We will derive the multi-solitary wave solutions analytically for Equation (1) using the bilinear method and discuss the propagation and interaction features based on the obtained analytic results.
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