Archive
2020, Volume 9
2019, Volume 8
2018, Volume 7
2017, Volume 6
2016, Volume 5
2015, Volume 4
2014, Volume 3
2013, Volume 2
2012, Volume 1




Volume 3, Issue 3, June 2014, Page: 70-77
On Expressive Construction of Solitons from Physiological Wave Phenomena
Nzerem Francis Egenti, Department of Mathematics & Statistics, University of Port Harcourt, Nigeria
Received: May 29, 2014;       Accepted: Jun. 30, 2014;       Published: Jul. 20, 2014
DOI: 10.11648/j.pamj.20140303.13      View  2797      Downloads  176
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.
Keywords
Mathematical, Bilinear, Asymptotic Expansion, Pulse Wave, Systolic and Diastolic
To cite this article
Nzerem Francis Egenti, On Expressive Construction of Solitons from Physiological Wave Phenomena, Pure and Applied Mathematics Journal. Vol. 3, No. 3, 2014, pp. 70-77. doi: 10.11648/j.pamj.20140303.13
Reference
[1]
T. Laleg, E. Crespeau, and M. Sorine, “Separation of arterial pressure into solitary waves and windkessel flow”, MCBMS’06, IFAC Reims,2006
[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.
[18]
J.M. Curry, “Solitions solution of integrable systems and Hirotha’s method”,The Havard college of Mathematics Review 2.1, 2008
[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.
Browse journals by subject