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A theory is developed relating to the stability of solitary-wave solutions of the so-called Benjamin-Ono equation. This equation was derived by Benjamin (5) as a model for the propagation of internal waves in an incompressible non-diffusive heterogeneous fluid for which the density is non-constant only within a layer whose thickness is much smaller than the total depth. In his article, Benjamin wrote in closed form the one-parameter family of solitary-wave solutions of his model equation whose stability will be the focus of attention presently.
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Bennett et al. (1983) studied this question.
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