Rouge waves in fluid-filled elastic tube

Chen Zhi-Min; Duan Wen-Shan

doi:10.7498/aps.69.20191308

Abstract

By the reductive perturbation method, we investigate the Rogue waves in a fluid-filled elastic tube. Based on a nonlinear Schrodinger equation obtained from a fluid-filled elastic tube, the rouge wave solution in the fluid-filled elastic tube is discussed. The characteristics of a single rouge waveare studied for this system. Then, the effects of the system parameters, such as the wave number k, the parameters $\epsilon$, the density of the fluid, the thickness of the elastic tube, the Yang's modulus of the elastic tube, and the radius of the elastic tube on the rouge wave are also investigated. Finally, the model is applied to the blood vessels of both animal and the human to ascertain the effects of the rouge wave in different arteries and vessels. The results of the present study may have potential applications in medical science.

Keywords:

Authors and contacts

College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Corresponding author: Duan Wen-Shan, duanws@126.com

Funds: Project Supported by the National Natural Science Foundation of China (Grants No. 11965019)

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References

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图 1 怪波振幅的密度图

Figure 1. The contour graph of a rogue wave solution image

DownLoad: Full-Size Img PowerPoint

图 2 不同时刻的怪波图像

Figure 2. The above picture shows the rouge wave for t = 0.1 s, t = 0.5 s and t = 0.9 s.

DownLoad: Full-Size Img PowerPoint

图 3 人体血管参数对怪波振幅的影响　(a)波数$ k $; (b)小参数$ \varepsilon $; (c)厚度$ h $, (d)液体密度$ \rho $; (e)杨氏模量$ E $; (f)半径$ a $

Figure 3. The effect of human vascular parameters on the amplitude of rouge waves:(a) $ k $; (b) $ \varepsilon $; (c) $ h $; (d) $ \rho $; (e) $ E $; (f) $ a $.

DownLoad: Full-Size Img PowerPoint

图 4 人体血管参数对怪波波速的影响　(a)波数$ k $; (b)小参数$ \varepsilon $; (c)厚度$ h $; (d)液体密度$ \rho $; (e)杨氏模量$ E $; (f)半径$ a $值

Figure 4. The effect of elastic tube parameters on the velocity of rouge waves: (a) $ k $; (b) $ \varepsilon $; (c) $ h $; (d) $ \rho $; (e) $ E $; (f) $ a $.

DownLoad: Full-Size Img PowerPoint

[1]	Zhen P F, Jia M 2018 Chin. Phys. B 27 120201 Google Scholar
[2]	Zhang X, Yong C 2018 Nonlinear Dyn. 93 1 Google Scholar
[3]	李淑青, 杨光晔, 李禄 2014 物理学报 63 10 Li S Q, Yang G Y, Li l 2014 Acta Phys. Sin. 63 10
[4]	Xin W, Chong L, Lei W 2017 J. Math. Anal. Appl. 449 1534 Google Scholar
[5]	Dewey J F, Ryan P D 2017 Proc. Natl. Acad. Sci. U.S.A. 114 E10639 Google Scholar
[6]	Onorato M, Residori S, Bortolozzo U, Montina A, Arecchi F T 2013 Phys. Rep. 528 47 Google Scholar
[7]	Yeom D I, Eggleton, Benjamin J 2007 Nature 450 53
[8]	Akhmediev N, Ankiewicz A, Taki M 2009 Phys. Lett. A 373 675 Google Scholar
[9]	Garrett C, Gemmrich J, Baschek B 2009 Phys. Today 15 3210
[10]	Draper L 1967 Mar. Geol. 5 133 Google Scholar
[11]	Akhmediev N, Soto-Crespo J, Ankiewicz A 2009 Phys. Rev. A 80 82
[12]	Kibler B, Chabchoub A, Gelash A, Akhmediev N, Zakharov V 2015 Phys. Rev. A 5 041026
[13]	Bailung H, Sharma S K, Nakamura Y 2011 Phys. Rev. Lett. 107 255005 Google Scholar
[14]	Moslem W M, Sabry R, El-Labany S K, Shukla P K 2011 Phys. Rev. E 84 066402 Google Scholar
[15]	Stenflo L, Marklund M 2009 J. Plasma Phys. 76 293
[16]	Efimov V B, Ganshin A N, Kolmakov G V, Mcclintock P V E, Mezhov-Deglin L P 2010 Eur. Phys. J. Spec. Top. 185 181 Google Scholar
[17]	Bludov Y V, Konotop V V, Akhmediev N 2010 Eur. Phys. J. Spec. Top. 185 169 Google Scholar
[18]	Schneider T M, Gibson J F, Burke J 2010 Phys. Rev. Lett. 104 104501 Google Scholar
[19]	Peregrine D H 1983 Anziam J. 25 16
[20]	Mohany A, Sadek O, Hassan M 2018 J. Fluid Struct. 79 171 Google Scholar
[21]	沈惠杰, 温激鸿, 郁殿龙, 温熙森 2009 物理学报 58 8357 Google Scholar Shen H J, Wen J H, Yu D L, Wen X S 2009 Acta Phys. Sin. 58 8357 Google Scholar
[22]	Demiray H 1996 B Math. Biol. 58 939 Google Scholar
[23]	Demiray H 2002 Appl. Math. Comput. 133 29
[24]	Demiray H 2008 Int. J. Nonlinear Mech. 43 241 Google Scholar
[25]	Antar N 2002 Int. J. Eng. Sci. 40 1179 Google Scholar
[26]	Duan W S, Wang B R, Wei R J 1997 Phys. Lett. A 224 154 Google Scholar
[27]	Lamb G L 1981 Adv. Math. 32 215
[28]	Sigeo Y 1987 J. Phys. Soc. Jpn. 56 506 Google Scholar
[29]	Paquerot J F, Remoissenet M 1994 Phys. Lett A 194 77 Google Scholar
[30]	Duan W S, Wang B R, Wei R J 1996 J. Phys. Soc. Jpn. 65 945 Google Scholar
[31]	Hammani K, Kibler B, Finot C, Akhmediev N, Dudley J M 2011 Opt. Lett. 36 112 Google Scholar
[32]	柳兆荣, 徐刚, 陈泳, 滕忠照, 覃开蓉 2003 应用数学和力学 24 205 Google Scholar Liu Z R, Xu G, Chen Y, Teng Z Z, Qin K R 2003 Adv. Appl. Math. Mech. 24 205 Google Scholar
[33]	Chuong C J, Fung Y C 1986 J. Biomech. Eng. 108 189 Google Scholar

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Vol. 69, Issue 1 - 2020-01-05

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