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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:
- reductive perturbation method /
- nonlinear Schrodinger equation /
- rouge wave /
- blood vessel
[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
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[7] Yeom D I, Eggleton, Benjamin J 2007 Nature 450 53
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[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
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[18] Schneider T M, Gibson J F, Burke J 2010 Phys. Rev. Lett. 104 104501
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[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
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[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
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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
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Liu Z R, Xu G, Chen Y, Teng Z Z, Qin K R 2003 Adv. Appl. Math. Mech. 24 205
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Google Scholar
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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
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.
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 $ .
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 $ . -
[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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