Abstract This paper studies the hydrodynamic solitons propagating along a long trough with a defective bed. The slight deviation from the plane in the bed serves as the depth defects. Based on the perturbation method, it finds that the free surface wave is governed by a Korteweg-de Vries (KdV) equation with a defect term (KdVD). The numerical calculations show that, for a single-convexity localized defect, the propagating soliton is decelerated as it comes into the defect region, and it is accelerated back to its initial velocity as it leaves, which has a dipole effect. As a result, its displacement is lagged in contrast to the uninfluenced one. And an up-step defect makes the propagating soliton decelerate simply. The opposite influence will occur for a single-concavity localized defect and a down-step one. The defect-induced influence on propagating hydrodynamic solitons depends on the polarity of defects, which agrees with that on non-propagating ones. However, the involved dipole effect of the single localized defect is not displayed in non-propagating cases.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10774072).
Cite this article:
Pan Jun-Ting(潘军廷), Chen Wei-Zhong(陈伟中), and Zheng Lu-Jie(郑鹭杰) Interactions between defects and propagating hydrodynamic solitons 2010 Chin. Phys. B 19 080304
[1]
Wu J R, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421
[2]
Denardo B, Wright W, Putterman S and Larraza A 1990 Phys. Rev. Lett. 64 1518
[3]
Jiang D S and She W L 2007 Acta Phys. Sin. 56 245 (in Chinese)
[4]
Cao L G, Lu D Q, Hu W, Yang P B, Zhu Y Q and Guo Q 2008 Acta Phys. Sin. 57 6365 (in Chinese)
[5]
Song L J, Li L and Zhou G S 2007 Chin. Phys. 16 148
[6]
Dai C Q and Zhou G Q 2007 Chin. Phys. 16 1201
[7]
Zheng H J, Liu S L and Xu J P 2007 Chin. Phys. 16 2023
[8]
Yang J R and Mao J J 2008 Chin. Phys. B 17 4337
[9]
Peng J Z, Yang H and Tang Y 2009 Chin. Phys. B 18 2364
[10]
Mei C C 1986 J. Fluid Mech. 162 53
[11]
Wu T Y T 1987 J. Fluid Mech. 184 75
[12]
Grimshaw R H J and Smyth N 1986 J. Fluid Mech. 169 429
[13]
Kakutani T 1971 J. Phys. Soc. Jpn. 30 272
[14]
Redekopp L G and You Z 1995 Phys. Rev. Lett. 74 5158
[15]
Zhu Y 1998 Journal of Hydrodynamics Ser. A 13 272 (in Chinese)
[16]
Yan J R and Tang Y 1996 Phys. Rev. E 54 6816
[17]
Yan J R, Tang Y, Zhou G H and Chen Z H 1998 Phys. Rev. E 58 1064
[18]
Yan J R, Ao S M and Yu H Y 2005 Chin. Phys. 14 28
[19]
Wang D L, Yan X H, Tang Y, Ding J W and Cao J X 2001 Acta Phys. Sin. 50 1201 (in Chinese)
[20]
Li H, Wang T J, Huang D X and Wang D N 2004 Chin. Phys. 13 1447
[21]
Ding N and Guo Q 2009 Chin. Phys. B 18 4298
[22]
Scharf R and Bishop A R 1991 Phys. Rev. A 43 6535
[23]
Braun O M and Kivshar Y S 1991 Phys. Rev. B 43 1060
[24]
Alexeeva N V, Barashenkov I V and Tsironis G P 2000 Phys. Rev. Lett. 84 3053
[25]
Chen W Z, Hu B B and Zhang H 2002 Phys. Rev. B 65 134302
[26]
Chen W Z, Zhu Y F and Lu L 2003 Phys. Rev. B 67 184301
[27]
Xu H, Chen W Z and Zhu Y F 2007 Phys. Rev. B 75 224303
[28]
Li H and Wang D N 2009 Chin. Phys. B 18 2659
[29]
Zhu W L, Luo L, He Y J and Wang H Z 2009 Chin. Phys. B 18 4319
[30]
Chen W Z, Lu L and Zhu Y F 2005 Phys. Rev. E 71 036622
[31]
Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1997 Numerical Recipes in C 2nd ed. (Cambridge: Cambridge University Press) pp. 714--722
Design and high-power test of 800-kW UHF klystron for CEPC Ou-Zheng Xiao(肖欧正), Shigeki Fukuda, Zu-Sheng Zhou(周祖圣), Un-Nisa Zaib, Sheng-Chang Wang(王盛昌), Zhi-Jun Lu(陆志军), Guo-Xi Pei(裴国玺), Munawar Iqbal, and Dong Dong(董东). Chin. Phys. B, 2022, 31(8): 088401.
No Suggested Reading articles found!
Viewed
Full text
Abstract
Cited
Altmetric
blogs
tweeters
Facebook pages
Wikipedia page
Google+ users
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.