Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients

doi:10.1088/1674-1056/abff31

中国物理B ›› 2021, Vol. 30 ›› Issue (11): 110202-110202.doi: 10.1088/1674-1056/abff31

Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients

Ying Yang(杨颖)¹, Yu-Xiao Gao(高玉晓)², and Hong-Wei Yang(杨红卫)^1,†

1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
2 Qingdao West Coast New Area Hospital of Traditional Chinese Medicine, Qingdao 266590, China

收稿日期:2021-03-17 修回日期:2021-04-07 接受日期:2021-05-08 出版日期:2021-10-13 发布日期:2021-10-22
通讯作者: Hong-Wei Yang E-mail:hwyang1979@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11975143), Nature Science Foundation of Shandong Province of China (Grant No. ZR2018MA017), the Taishan Scholars Program of Shandong Province, China (Grant No. ts20190936), and the Shandong University of Science and Technology Research Fund (Grant No. 2015TDJH102).

Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients

Ying Yang(杨颖)¹, Yu-Xiao Gao(高玉晓)², and Hong-Wei Yang(杨红卫)^1,†

1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
2 Qingdao West Coast New Area Hospital of Traditional Chinese Medicine, Qingdao 266590, China

Received:2021-03-17 Revised:2021-04-07 Accepted:2021-05-08 Online:2021-10-13 Published:2021-10-22
Contact: Hong-Wei Yang E-mail:hwyang1979@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11975143), Nature Science Foundation of Shandong Province of China (Grant No. ZR2018MA017), the Taishan Scholars Program of Shandong Province, China (Grant No. ts20190936), and the Shandong University of Science and Technology Research Fund (Grant No. 2015TDJH102).

摘要/Abstract

摘要： The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics, physics, biological fluid mechanics, oceanography, etc. Using the reductive perturbation theory and long wave approximation, the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrödinger (NLS) equations with variable coefficients. The third-order nonlinear Schrödinger equation is degenerated into a completely integrable Sasa-Satsuma equation (SSE) whose solutions can be used to approximately simulate the real rogue waves in the vessels. For the first time, we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves. Based on the traveling wave solutions of the fourth-order nonlinear Schrödinger equation, we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall. Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube. The high-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.

关键词: rogue wave, variable-coefficients high-order nonlinear Schrö, dinger equation, deformable blood vessels, Sasa-Satsuma equation

Abstract: The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics, physics, biological fluid mechanics, oceanography, etc. Using the reductive perturbation theory and long wave approximation, the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrödinger (NLS) equations with variable coefficients. The third-order nonlinear Schrödinger equation is degenerated into a completely integrable Sasa-Satsuma equation (SSE) whose solutions can be used to approximately simulate the real rogue waves in the vessels. For the first time, we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves. Based on the traveling wave solutions of the fourth-order nonlinear Schrödinger equation, we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall. Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube. The high-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.

Key words: rogue wave, variable-coefficients high-order nonlinear Schrö, dinger equation, deformable blood vessels, Sasa-Satsuma equation

中图分类号: (Partial differential equations)

02.30.Jr

03.65.Ge (Solutions of wave equations: bound states)

Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients[J]. 中国物理B, 2021, 30(11): 110202-110202.

Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients[J]. Chin. Phys. B, 2021, 30(11): 110202-110202.

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Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients

Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients

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