Painlev analysis and integrability of systems of nonlinear partial differential equations

The method of Painleve analysis is introduced and used to explore the integrability of certain physically significant nonlinear partial differential equations (nPDEs). These nPDEs include the Burgers’ equation, Korteweg-de Vries equation (KdV) and nonlinear Klein-Gordon equation. Furthermore, it is...

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主要作者:	Md. Nasrudin, Farah Suraya
格式:	Thesis
语言:	English
出版:	2009
主题:	QA Mathematics
在线阅读:	http://eprints.utm.my/id/eprint/18277/1/FarahSurayaNasrudinMFSA2010.pdf
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spelling	my-utm-ep.182772018-06-25T09:00:10Z Painlev analysis and integrability of systems of nonlinear partial differential equations 2009 Md. Nasrudin, Farah Suraya QA Mathematics The method of Painleve analysis is introduced and used to explore the integrability of certain physically significant nonlinear partial differential equations (nPDEs). These nPDEs include the Burgers’ equation, Korteweg-de Vries equation (KdV) and nonlinear Klein-Gordon equation. Furthermore, it is shown primarily that this Painleve test is intended to determine necessary conditions for such class of nPDEs to have the Painleve property. However, the nonlinear Klein-Gordon equation is shown instead to be integrable with respect to the Weak Painlevé test. 2009 Thesis http://eprints.utm.my/id/eprint/18277/ http://eprints.utm.my/id/eprint/18277/1/FarahSurayaNasrudinMFSA2010.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science [1] Ince, E. L. (1956). Ordinary Differential Equations. New York: Dover. [2] Kovalevskaya, S. (1890). Sur une propriété du système d'équations différentielles qui définit la rotation d'un corps solide autour d'un point fixe. Acta Math. 14, 81- 93. [3] Ablowitz, M. J., Ramani, A. and Segur, H. (1980). A connection Between Nonlinear Equations and Ordinary Differential Equations of P-Type I, J. Math. Phys. 21,715. [4] Whitham, G. B. (1974). Linear and Non-linear Waves. Ney York: Wiley. [5] McLeod, J. B. and Olver, P. J. (1983). The Connection Between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painleve Type, SIAM J. Math. Anal. 14, 488-506. [6] Chudnovsky, D. V. (1979). Riemann Monodromy Problem, Isomonodromy Deformation Equations and Completely Integrable Systems. In Bardos, C. and Bessis, D. (Eds.) Bifurcation Phenomena in Mathematical Physics (C.Bardos and D. Bessis, eds.) New York: Reidel. [7] Weiss, J., Tabor, M. and Carnevale, G. (1983). The Painlevé Property for Partial Differential Equations. J. Math. Phys.. 24, 522-526. [8] Fuchs, R. (1907). Uber lineare homogene differentialgleichungen zweiter ordnung mit drei im endlich gelegene wesentlich singularen Stellen. Math. Ann. 63, 301–321. [9] Nishioka, K. (1988). A note on the transcendency of Painlevé's first transcendent. Nagoya Mathematical Journal. 109, 63–67. [10] Umemura, H. (1989). On the irreducibility of Painlevé differential equations. Sugaku Expositions. 2, 231–252. [11] Ramani, A., Grammaticos, B. and Bountis, T. (1989). The Painlevé Property and Singular Analysis of Integrable and Non-integrable Systems. Physics Reports. 180, 159-245. [12] Hereman, W. (1998). The Painlevé Integrability Test. In Grabmeier, J. et al., (Eds.) Computer Algebra in Germany. (pp.211-232). New York: Springer- Verlag. [13] Pierce, V. (1999). Painleve Analysis and Integrability. The Nonlinear Journal. 1, 41-49. [14] Chen, H. H. and Lin, J. E. (1988). Integrability of Nonlinear Wave, Annals of the New York Academy of Sciences, 536, 91-99. [15] Hietarinta, J. (1987). A Search of Bilinear Equations Passing Hirota's Three- Soliton Condition: III. Sine-Gordon-Type Bilinear Equations, J. Math. Phys., 28, 1732, 2094, 2586
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Md. Nasrudin, Farah Suraya Painlev analysis and integrability of systems of nonlinear partial differential equations
description	The method of Painleve analysis is introduced and used to explore the integrability of certain physically significant nonlinear partial differential equations (nPDEs). These nPDEs include the Burgers’ equation, Korteweg-de Vries equation (KdV) and nonlinear Klein-Gordon equation. Furthermore, it is shown primarily that this Painleve test is intended to determine necessary conditions for such class of nPDEs to have the Painleve property. However, the nonlinear Klein-Gordon equation is shown instead to be integrable with respect to the Weak Painlevé test.
format	Thesis
qualification_level	Master's degree
author	Md. Nasrudin, Farah Suraya
author_facet	Md. Nasrudin, Farah Suraya
author_sort	Md. Nasrudin, Farah Suraya
title	Painlev analysis and integrability of systems of nonlinear partial differential equations
title_short	Painlev analysis and integrability of systems of nonlinear partial differential equations
title_full	Painlev analysis and integrability of systems of nonlinear partial differential equations
title_fullStr	Painlev analysis and integrability of systems of nonlinear partial differential equations
title_full_unstemmed	Painlev analysis and integrability of systems of nonlinear partial differential equations
title_sort	painlev analysis and integrability of systems of nonlinear partial differential equations
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2009
url	http://eprints.utm.my/id/eprint/18277/1/FarahSurayaNasrudinMFSA2010.pdf
_version_	1747815235915350016

Painlev analysis and integrability of systems of nonlinear partial differential equations

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