Re-visiting the head-on collision problem between two solitary waves in shallow water
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Tarih
2015-03
Yazarlar
Dergi Başlığı
Dergi ISSN
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Yayıncı
Pergamon-Elsevier Science Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Upon discovering the wrongness of the statement "although this term does not cause any secularity for this order it will cause secularity at higher order expansion, therefore, that term must vanish" by Su and Mirie [4], in the present work, we studied the head-on collision of two solitary waves propagating in shallow water by introducing a set of stretched coordinates in which the trajectory functions are of order of epsilon(2), where epsilon is the smallness parameter measuring non-linearity. Expanding the field variables and trajectory functions into power series in epsilon, we obtained a set of differential equations governing various terms in the perturbation expansion. By solving them under non-secularity condition we obtained the evolution equations and also the expressions for phase functions. By seeking a progressive wave solution to these evolution equations we have determined the speed correction terms and the phase shifts. As opposed to the result of Su and Mine [4] and similar works, our calculations show that the phase shifts depend on both amplitudes of the colliding waves.
Açıklama
Anahtar Kelimeler
Head-on collision, Solitary waves in water, Phase shifts, Fluid, Korteweg-de Vries equation, Solitons, Water waves, Differential equations, Phase shift, Correction terms, Evolution equations, Higher order expansions, Parameter measuring, Perturbation expansions, Progressive wave solutions, Trajectory functions
Kaynak
International Journal Of Non-Linear Mechanics
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
69
Sayı
Künye
Özden, A. E. & Demiray, H. (2015). Re-visiting the head-on collision problem between two solitary waves in shallow water. International Journal of Non-Linear Mechanics, 69, 66-70. doi:10.1016/j.ijnonlinmec.2014.11.022
