An application of modified reductive perturbation method to long water waves

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Tarih

2011-12

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Yayıncı

Pergamon-Elsevier Science Ltd

Erişim Hakkı

info:eu-repo/semantics/closedAccess

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Özet

In this work, we extended the application of "the modified reductive perturbation method" to long water waves and obtained the governing equations as the KdV hierarchy. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameter c(1) so as to remove the possible secularities that might occur. The present method is seen to be fairly simple as compared to the renormalization method [Kodama, Y., & Taniuti, T. (1977). Higher order approximation in reductive perturbation method 1. Weakly dispersive system. Journal of Physics Society of Japan, 45, 298-310] and the multiple scale expansion method [Kraenkel, R. A., Manna, M. A., & Pereira, J. G. (1995). The Korteweg-deVries hierarchy and long water waves. Journal of Mathematics Physics, 36, 307-320].

Açıklama

Anahtar Kelimeler

Modified reductive perturbation method, Water waves, Korteweg-de Vries hierarchy, Higher-order terms, Solitary waves, Korteweg-de Vries equation, Solitons, Dispersive systems, Evolution equations, Governing equations, Higher-order approximation, KdV hierarchy, Korteweg-de Vries, Long water waves, Multiple-scale expansion, Reductive perturbation methods, Renormalization methods, Scale parameter, Travelling wave solution, Hydrodynamics, Waves, Perturbation techniques

Kaynak

International Journal of Engineering Science

WoS Q DeÄŸeri

Q1

Scopus Q DeÄŸeri

Q1

Cilt

49

Sayı

12

Künye

Demiray, H. (2011). An application of modified reductive perturbation method to long water waves. International Journal of Engineering Science, 49(12), 1397-1403. doi:10.1016/j.ijengsci.2011.04.002