This paper is a study of nonlinear waves in a fluid-filled elastic tube, whose wall material satisfies the stress-strain law given by the kinetic theory of rubber. The results of this study have extended the scope of this subject, which has been limited to dealing with unidirectional solitary waves only (Olsen & Shapiro 1967), by establishing an exact theory for bidirectional solitions of arbitrary shape. This class of solitons has several remarkable characteristics. These solitons may have arbitrary shape and arbitrary polarity (upward or downward), and all propagate with the same phase velocity. The last feature of wave velocity renders the interactions impossible between unidirectional waves. However, the present new theory shows that bidirectional waves can have head-on collision through which our {it exact} solution leaves each wave a specific phase shift as a permanent mark of the waves having made the nonlinear encounter.
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