Nonautonomous bright soliton solutions on continuous wave and cnoidal wave backgrounds in blood vessels

2013 ◽  
Vol 75 (1-2) ◽  
pp. 201-207 ◽  
Author(s):  
Hua-Jie Jiang ◽  
Jia-Jie Xiang ◽  
Chao-Qing Dai ◽  
Yue-Yue Wang
2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.


2021 ◽  
Author(s):  
Duplex Steve MBIEDA PETMEGNI ◽  
Frank Gaetan Mbieda Ngomegni ◽  
Alain Dikande ◽  
B. Z. Essimbi

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.


Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.


2016 ◽  
Vol 71 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Hengchun Hu ◽  
Xiao Hu ◽  
Bao-Feng Feng

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.


2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.


2009 ◽  
Vol 26 (12) ◽  
pp. 120308 ◽  
Author(s):  
Liu Hong ◽  
He Dai-Hai ◽  
Lou Sen-Yue ◽  
He Xian-Tu

VASA ◽  
2003 ◽  
Vol 32 (4) ◽  
pp. 225-233 ◽  
Author(s):  
Bollinger ◽  
Partsch

Christian Doppler was born 200 years ago in Salzburg, Austria, on November 29, 1803, worked in Prague and Vienna and died 150 years ago in Venice. In an article of eight pages he described the principle, which made him famous. It appeared in 1842 with the exotic title: “On the Coloured Light of the Double Stars and Certain Other Stars of the Heaven”. The validity of his principle for velocity measurement was confirmed by trumpet sounds produced on a train moving towards and away from the observer. Around 1960 Japanese scientists suggested that flow velocity in blood vessels could be determined by analysing the difference of frequency between emitted and backscattered ultrasound. Rushmer and coworkers built machines suitable for medicine in Seattle, where Eugene Strandness recognized their potential and applied them in first studies. In 1967 the technique jumped to Europe and started to be used worldwide. Already by using continuous wave ultrasound it was possible to diagnose occlusive disease of neck and limb arteries, venous thrombosis and valvular insufficiency with accuracy. Measurements of poststenotic ankle blood pressure were facilitated by Doppler sensing. Over the years more sophisticated instruments were developed. Pulsed emission of ultrasound waves opened a way to study flow velocity profiles across large vessels. By combining the method with A or B mode ultrasound blood flow could be quantified and finally perfused segments of blood vessels visualized. Duplex scanning in its simple and then in its colour coded version is nowadays the standard non-invasive technique that nobody would like to miss. Vascular territories like intracranial, renal and intestinal arteries can also be explored. For the assessment of microvascular flow in skin and mucosae laser Doppler instruments were introduced.


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