On Expressive Construction of Solitons from Physiological Wave Phenomena

Nzerem Francis Egenti

doi:doi:10.11648/j.pamj.20140303.13

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On Expressive Construction of Solitons from Physiological Wave Phenomena

Nzerem Francis Egenti

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 3)

Received: 29 May 2014 Accepted: 30 June 2014 Published: 20 July 2014

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Abstract

Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase. This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 3)
DOI	10.11648/j.pamj.20140303.13
Page(s)	70-77
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Mathematical, Bilinear, Asymptotic Expansion, Pulse Wave, Systolic and Diastolic

References

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[2]	M.Thiriet, Anatomy and Physiology of the Circulatory And Ventilatory Systems, Springer, 2013.
[3]	A. Babin, and A. Figotin, “Linear superposition in nonlinear wave dynamics” Rev. Math. Phys. 18, 971 (2006). DOI: 10.1142/S0129055X06002851,
[4]	D. J. Korteweg, and G. de Vries, "On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves", Philosophical Magazine 39 (240): 422–443, 1895 doi:10.1080/14786449508620739
[5]	T-M. Laleg, E. Crespeau, and M. Sorine, “Seperation of arterial pressure into solitary waves and windkessel flow”, Modeling and Control in Biomedical Systems, Volume 6, Part 1.pp105-110,2006, doi:10.3182/20060920-3-FR-2912.0002
[6]	F.E. Nzerem and H.N. Alozie, “The Underlying Physiology of Arterial Pulse Wave Morphology in Spatial Domain ”,Applications and Applied Mathematics: Vol. 8, Issue 2, , pp. 495 – 505,2013
[7]	F.E. Nzerem and H.C. Ugorji, “Arterial Pulse Waveform under the watch of Left Ventricular Ejection time: A physiological outlook”, Mathematical Theory and Modeling ,Vol.4, No.4, pp 119-128, 2014
[8]	N.J. Zabusky and M.A. Porter, Solition, Scholarpedia, 5(8):2086, 2010.
[9]	C. S.Gardner, J. M. Greene, M.D.Kruskal and R.M. Miura, "Method for Solving the Korteweg-deVries Equation", Physical review letters 19: pp 1095–1097, 1967, Bibcode:1967PhRvL..19.1095G, doi:10.1103/PhysRevLett.19.1095
[10]	C. S.Gardner, J. M. Greene, M.D.Kruskal and R.M. Miura,), "Korteweg-deVries equation and generalization. VI. Methods for exact solution", Comm. Pure Appl. Math. 27: pp 97–133, 1974. doi:10.1002/cpa.3160270108, MR 0336122
[11]	W. Malfliet, “The tanh method: a tool for solving certain class of nonlinear evolution and wave equations”, J.Comp. Appl. Math. pp 164-165, 2004
[12]	W. Malfliet, “Solitary wave solutions of nonlinear wave equations”, Am. J. Phys. 60, pp 650-654, 1992
[13]	R. Hirota, “Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons”, Phys. Rev. Lett. 27, 1192, 1971. DOI: http://dx.doi.org/10.1103/PhysRevLett.27.1192
[14]	H. Song and L. Tao, “Soliton solutions for Korteweg-de Vries equation by homotopy analysis method”, AnziamJ (CTAC) pp C152-C158,2008
[15]	L. Zou and Z. Zong, “Homotopy analysis method for some nonlinear water wave problems” [Online] http://www.docin.com/p-521846913.html, Retrieved 26May, 2014
[16]	W. Hereman and W. Malfliet, “The Tanh Method: atool to solve nonlinear partial differential equations with symbolic software” [Online]:http://inside.mines.edu/~whereman/papers/Hereman-Malfliet-WMSCI- 2005.pdf retrieved 27May, 2014.
[17]	J. Hietarinta,” Hirota's bilinear method and soliton solutions”, Physics AUC, vol.15 (part1), 2005.
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[19]	W.Hereman, and W. Zhuang, “Symbolic Computation of Solitons via Hirota’s Bilinear Method”. [Online] Available: http://inside.mines.edu/~whereman/papers/Hereman-Zhuang-Hirota- Method-Preprint-1994.pdf
[20]	P.G. Drazin and R.S. Johnson (1989), Solitions: an introduction, Cambridge University Press.

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APA Style

Nzerem Francis Egenti. (2014). On Expressive Construction of Solitons from Physiological Wave Phenomena. Pure and Applied Mathematics Journal, 3(3), 70-77. https://doi.org/10.11648/j.pamj.20140303.13

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ACS Style

Nzerem Francis Egenti. On Expressive Construction of Solitons from Physiological Wave Phenomena. Pure Appl. Math. J. 2014, 3(3), 70-77. doi: 10.11648/j.pamj.20140303.13

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AMA Style

Nzerem Francis Egenti. On Expressive Construction of Solitons from Physiological Wave Phenomena. Pure Appl Math J. 2014;3(3):70-77. doi: 10.11648/j.pamj.20140303.13

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@article{10.11648/j.pamj.20140303.13,
  author = {Nzerem Francis Egenti},
  title = {On Expressive Construction of Solitons from Physiological Wave Phenomena},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {3},
  pages = {70-77},
  doi = {10.11648/j.pamj.20140303.13},
  url = {https://doi.org/10.11648/j.pamj.20140303.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140303.13},
  abstract = {Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase.  This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.},
 year = {2014}
}

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TY  - JOUR
T1  - On Expressive Construction of Solitons from Physiological Wave Phenomena
AU  - Nzerem Francis Egenti
Y1  - 2014/07/20
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140303.13
DO  - 10.11648/j.pamj.20140303.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 70
EP  - 77
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140303.13
AB  - Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase.  This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.
VL  - 3
IS  - 3
ER  -

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Author Information

Nzerem Francis Egenti

Department of Mathematics & Statistics, University of Port Harcourt, Nigeria

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APA Style

Nzerem Francis Egenti. (2014). On Expressive Construction of Solitons from Physiological Wave Phenomena. Pure and Applied Mathematics Journal, 3(3), 70-77. https://doi.org/10.11648/j.pamj.20140303.13

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ACS Style

Nzerem Francis Egenti. On Expressive Construction of Solitons from Physiological Wave Phenomena. Pure Appl. Math. J. 2014, 3(3), 70-77. doi: 10.11648/j.pamj.20140303.13

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AMA Style

Nzerem Francis Egenti. On Expressive Construction of Solitons from Physiological Wave Phenomena. Pure Appl Math J. 2014;3(3):70-77. doi: 10.11648/j.pamj.20140303.13

Copy | Download

@article{10.11648/j.pamj.20140303.13,
  author = {Nzerem Francis Egenti},
  title = {On Expressive Construction of Solitons from Physiological Wave Phenomena},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {3},
  pages = {70-77},
  doi = {10.11648/j.pamj.20140303.13},
  url = {https://doi.org/10.11648/j.pamj.20140303.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140303.13},
  abstract = {Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase.  This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - On Expressive Construction of Solitons from Physiological Wave Phenomena
AU  - Nzerem Francis Egenti
Y1  - 2014/07/20
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140303.13
DO  - 10.11648/j.pamj.20140303.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 70
EP  - 77
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140303.13
AB  - Physiological waves, much like the waves of some other physical phenomena, consist of non-linear and dispersive terms. In studies involving patho-physiology, models on arterial pulse waves indicate that the waveforms behave like solitons. The Korteweg-deVrie (KdV) equation, which is known to admit soliton solutions, is seen to hold well for arterial pulse waves. The foregoing underpins the need for detailed knowledge of the construction of solitons. In the light of this, plane wave solution would fail to yield the desired goal, let alone where arterial pulse waves are physiological waves that decompose into a travelling wave representing fast transmission phenomena during systolic phase and a windkessel term representing slow transmission phenomena during diastolic phase.  This paper elucidates the construction of the solitons that arise from the so called KdV equation. The goal is to enhance an authentic analysis of soliton-based clinical details.
VL  - 3
IS  - 3
ER  -

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