1 sonuçlar
Arama Sonuçları
Listeleniyor 1 - 1 / 1
Yayın Head-on collisions of solitary waves(Işık Üniversitesi, 2015-12-11) Özden, Ali Erinç; Demiray, Hilmi; Işık Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Doktora ProgramıThe interaction of solitary waves in various physical media is a long time studied subject in nonlinear wave theory. For overtaking collision between solitary waves, one can use the inverse scattering transform method to obtain the overtaking colliding effect of solitary waves. However, for the head-on collision between solitary waves, one must employ some kind of asymptotic expansion to solve the original field equations. This thesis addresses head-on collision problem between two solitary waves. The head-on collision of solitary waves in shallow water is re-examined upon discovering the wrongness of the statement about the secular terms in the pioneering work of Su and Mirie (J. Fluid Mech., 98:509-525, 1980). In the first part, based on the above argument, the head-on collision of two solitary waves propagating in shallow water is studied by introducing a set of stretched coordinates that includes some unknown trajectory functions which are to be determined so as to remove secularities that might occur in the solution. Expanding the field variables and trajectory functions into power series, a set of differential equations governing various terms in the perturbation expansion is obtained. By solving them under non-secularity condition, the evolution equations and also the expressions for phase shifts are determined. As opposed to the result of previous studies our calculation shows that the phase shifts depend on amplitudes of both colliding waves. In the second part, the head-on-collision of solitary waves in shallow water theory is examined through the use of extended Poincaré-Lighthill-Kuo(PLK) method. Following a similar procedure with the previous part, the speed correction terms and the trajectory functions are determined. The result obtained here is exactly same with that found in the first part. In the third part, the head-on collision of the solitary waves in fluid-filled elastic tubes is studied by employing the extended PLK method. Pursuing the procedure in the previous part, the speed correction terms and the trajectory functions are obtained. The results of our calculation show that both the evolution equations and the phase shifts are quite different from those of Xue (Phys. Lett. A, 331:409-413, 2004). As opposed to the result of previous works on the same subject, the phase shifts depend on the amplitudes of both colliding waves.
