Head-on collision of solitary waves in fluid-filled elastic tubes

Abstract

In the present work, by employing the field 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 effects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solution. Expanding these unknown functions and the field variables into power series of the smallness parameter and introducing the resulting expansions into the field equations we obtained the sets of partial differential equations. By solving these differential equations 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 different 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.

Head-on collision of electron acoustic solitary waves in a plasma with nonextensive hot electrons

“…On the other hand, we know that one of the striking properties of solitons is their asymptotic preservation of form when they undergo a collision, as was first remarked by Zabusky and Kruskal (1965). For the collision of solitary waves, the solution of two solitary waves of two Kortewege-de Vries (KdV) equations, which are valid for long waves, can explain the resonance phenomena, which have been observed in the laboratory in shallow water wave experiments (Maxworthy 1980), in plasma experiments (Nakamura et al 1999), in two-core optical fiber (Tsang et al 2004) and in fluid-filled elastic tubes (Demiray 2005). Some authors (Demiray 2005;Su and Mirie 1980) have studied the head-on collision of solitary waves in different media by using the extended Poincaré-Lighthill-Kuo (PLK) perturbation method (Jeffery and Kawahawa 1982).…”

“…For the collision of solitary waves, the solution of two solitary waves of two Kortewege-de Vries (KdV) equations, which are valid for long waves, can explain the resonance phenomena, which have been observed in the laboratory in shallow water wave experiments (Maxworthy 1980), in plasma experiments (Nakamura et al 1999), in two-core optical fiber (Tsang et al 2004) and in fluid-filled elastic tubes (Demiray 2005). Some authors (Demiray 2005;Su and Mirie 1980) have studied the head-on collision of solitary waves in different media by using the extended Poincaré-Lighthill-Kuo (PLK) perturbation method (Jeffery and Kawahawa 1982). Eslami et al (2011) investigated the head-on collision of ion-acoustic solitary waves in plasma consisting of cold ions, nonextensive electrons and thermal.…”

Collisional phase shifts between two colliding solitary waves in a three-dimensional magnetized dusty plasma

“…17,18 It is also found that collision of solitary waves has other practical applications, for example, in fluid-filled elastic tubes, 19 two-core optical fiber, 20 and polyacetylene, 21 to name only a few. The importance of collision of solitary waves attracts many researchers to concern about it.…”

Head-on collision of ion acoustic solitary waves in an electron-positron-ion plasma with superthermal electrons

“…For the collision of solitary waves, the solution of two solitary waves of two Kortewege-de Vries ͑KdV͒ equations, which are valid for long waves, can explain the resonance phenomena, which have been observed in the laboratory in shallow water wave experiments, 34 in plasma experiments, 35 in two-core optical fiber, 36 and in fluid-filled elastic tubes. 37 Accordingly, the importance of the collision of solitary waves attracts many investigators. [38][39][40][41][42][43][44][45] It is well known that one of the striking properties of solitons is their asymptotic preservation of form when they undergo a head-on collision ͑i.e., the angle between two propagation directions of two solitary waves is equal to ͒, as first remarked by Zabusky and Kruskal.…”