Soliton solutions of generalized $$(3+1)$$-dimensional Yu–Toda–Sasa–Fukuyama equation using Lie symmetry analysis

Jadaun, Vishakha; Singh, Nitin Raja

doi:10.1007/s13324-020-00385-0

Cited by 15 publications

(9 citation statements)

References 32 publications

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“…Nonlinear evolution equations (NLEEs) have been used to explore varied nonlinear phenomena present in scientific inquiry domain including its technological perspective. The scientific disciplines such as fluid dynamics, ionoacoustics, optics and solid state physics, among others utilize the potential of NLEEs [18][19][20][21][22][23][24] with crucial results in integrable systems and nonlinear dynamics. NLEEs are used to explain dispersion, dissipation, diffusion and convection processes.…”

Section: The Structural Characteristics Of Imh Type 2 Includementioning

confidence: 99%

Interaction between Conformational Features and Hemodynamic Flows affecting Progression of Aortic Aneurysm and Dissection Disorders

Jadaun¹,

Singh

2022

Preprint

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Hemodynamic flows are subjected to quasi-periodic velocity modulations. Currently, there is no methodology to predict the rate of progression of aortic aneurysm and dissection disorders. In this paper, the association between conformational features of the vessel wall and intra-luminal hemodynamic flows is explored to understand shear forces affecting the structural integrity of the vessel wall. The infinitesimal component of the vessel wall with cystic medial necrosis in tunica media is considered as nonlinear ballooning in the aorta with aortic aneurysm and dissection disorders. Assuming the hemodynamic system as a finite dissipative system, we frame the equation of the vessel wall of the aorta as well as lesion related to aortic aneurysm and dissection disorders. We introduce the main results for the generalized (3+1)-dimensional nonlinear evolution equation, using the Lie group of transformations method. Furthermore, we discuss the implications of traveling wave solutions and the shape, height, and width of the aneurysm to describe the impact of ballooning on hemodynamic flow in the aorta with aortic aneurysm and dissection disorders. We find that cumulative accretion of potential energy contributes to the creation of bright soliton in non-ballooned regions. The wave speed is minimum at the center of the ballooned region and maximum at the center of the non-ballooned region of the aorta. Interactions of topological defects and multi-breathers cause thrombus formation and/or turbulent flow. Interaction between breathers and standing waves is associated with thrombus formation.

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Section: The Structural Characteristics Of Imh Type 2 Includementioning

confidence: 99%

Interaction between Conformational Features and Hemodynamic Flows affecting Progression of Aortic Aneurysm and Dissection Disorders

Jadaun¹,

Singh

2022

Preprint

Self Cite

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“…Nonlinear Evolution Equations and Soliton Solutions. Nonlinear evolution equations (NLEEs) have been perused to address nonlinear phenomena in various branches of sciences [34][35][36][37][38][39] including biology and medicine. NLEE explains permeation of two-layer fluid comprised of blood and hypoxia inducible factor -1α in dispersive media.…”

Section: 3mentioning

confidence: 99%

Progression of Aortic Dissection: An Application of Soliton Solutions of Nonlinear Evolution Equation in (3+1)-Dimensions

Jadaun¹,

Singh²

2021

Preprint

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Aortic dissection is a serious pathology involving the vessel wall of the aorta with significant societal impact. To understand aortic dissection we explain the role of the dynamic pathology in the absence or presence of structural and/or functional abnormalities. We frame a differential equation to evaluate the impact of mean blood pressure on the aortic wall and prove the existence and uniqueness of its solution for homeostatic recoil and relaxation for infinitesimal aortic tissue. We model and analyze generalized (3+1)-dimensional nonlinear partial differential equation for aortic wave dynamics. We use the Lie group of transformations on this nonlinear evolution equation to obtain invariant solutions, traveling wave solutions including solitons. We find that abnormalities in the dynamic pathology of aortic dissection act as triggers for the progression of disease in early-stage through the formation of soliton-like pulses and their interaction. We address the role of unstable wavefields in waveform dynamics when waves are unidirectional. Moreover, the notion of dynamic pathology within the domain of vascular geometry may explain the evolution of aneurysms in cerebral arteries and cardiomyopathies even in the absence of anatomical and physiological abnormalities.

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“…In addition to mathematics, nonlinear phenomena are involved in many fields, such as atmospheric physics, optical fiber communication, biophysics, hydrodynamics and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Because of its important application value, the research of nonlinear phenomena has become a hot spot.…”

Section: Introductionmentioning

confidence: 99%

Superposition solutions to a (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like equation

Fan¹,

Bao²

2022

Phys. Scr.

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In this paper, the superposition solutions of (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like(vcSTOL) equation are studied. The equation can illustrate various difficult sciences areas. Due to the wide application, it is very important to find the exact solutions of it. By introducing transformation, the equation is transformed into bilinear form. We use variable separation method and trial function method to obtain the superposition solutions of the equation containing different functions and forms. The images are drawn with the help of symbolic computing system Mathematica, and the properties of the solutions are analyzed. The analysis shows that different functions will affect the overall shape of waves, including the interaction between waves, the size, the direction and the number of waves, which can get more new phenomena. To our knowledge, those types of superposition solutions of (3+1)-dimensional vcSTOL equation mentioned in our work by variable separation method have not been reported before. Furthermore, we add the square terms to the expansion function, so that the obtained solutions have the characteristics of Lump solution, which has not been done in the previous literatures.

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Soliton solutions of generalized $$(3+1)$$-dimensional Yu–Toda–Sasa–Fukuyama equation using Lie symmetry analysis

Cited by 15 publications

References 32 publications

Interaction between Conformational Features and Hemodynamic Flows affecting Progression of Aortic Aneurysm and Dissection Disorders

Interaction between Conformational Features and Hemodynamic Flows affecting Progression of Aortic Aneurysm and Dissection Disorders

Progression of Aortic Dissection: An Application of Soliton Solutions of Nonlinear Evolution Equation in (3+1)-Dimensions

Superposition solutions to a (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like equation

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