期刊
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
卷 49, 期 12, 页码 1397-1403出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2011.04.002
关键词
Modified reductive perturbation method; Water waves; Korteweg-de Vries hierarchy
资金
- Turkish Academy of Science (TUBA)
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]. (C) 2011 Elsevier Ltd. All rights reserved.
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