HEAD-ON COLLISION OF THE SOLITARY WAVES IN FLUID-FILLED ELASTIC TUBES

A. E. OZDEN1, H. DEMIRAY1

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Abstract

In the present work, by employing the eld equations given in [15] and the extended PLK method derived in [9], we have studied the head-on collision of solitary waves in arteries. Introducing a set of stretched coordinates which include some unknown functions characterizing the higher order dispersive eects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solu- tion. Expanding these unknown functions and the eld variables into power series of the smallness parameter  and introducing the resulting expansions into the eld equations we obtained the sets of partial dierential equations. By solving these dierential equa- tions and imposing the requirements for the removal of possible secularities we obtained the speed correction terms and the trajectory functions. The results of our calculation show that both the evolution equations and the phase shifts resulting from the head-on collision of solitary waves are quite dierent from those of Xue [15], who employed the incorrect formulation of Su and Mirie [4]. As opposed to the result of previous works on the same subject, in the present work the phase shifts depend on the amplitudes of both colliding waves.

Keywords

Elastic tubes, Solitary waves, Head-on collision, Extended PLK Method.