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Numerical solution of Prandtl's lifting-line equation /Budi Kurniawan. January 1992 (has links) (PDF)
Thesis (M. Sc.)--University of Adelaide, Dept. of Applied Mathematics, 1992. / Includes bibliographical references (leaves 79-80).
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An Application of the Inverse Scattering Transform to some Nonlinear Singular Integro-Differential Equations.Scoufis, George January 1999 (has links)
ABSTRACT The quest to model wave propagation in various physical systems has produced a large set of diverse nonlinear equations. Nonlinear singular integro-differential equations rank amongst the intricate nonlinear wave equations available to study the classical problem of wave propagation in physical systems. Integro-differential equations are characterized by the simultaneous presence of integration and differentiation in a single equation. Substantial interest exists in nonlinear wave equations that are amenable to the Inverse Scattering Transform (IST). The IST is an adroit mathematical technique that delivers analytical solutions of a certain type of nonlinear equation: soliton equation. Initial value problems of numerous physically significant nonlinear equations have now been solved through elegant and novel implementations of the IST. The prototype nonlinear singular integro-differential equation receptive to the IST is the Intermediate Long Wave (ILW) equation, which models one-dimensional weakly nonlinear internal wave propagation in a density stratified fluid of finite total depth. In the deep water limit the ILW equation bifurcates into a physically significant nonlinear singular integro-differential equation known as the 'Benjamin-Ono' (BO) equation; the shallow water limit of the ILW equation is the famous Korteweg-de Vries (KdV) equation. Both the KdV and BO equations have been solved by dissimilar implementations of the IST. The Modified Korteweg-de Vries (MKdV) equation is a nonlinear partial differential equation, which was significant in the historical development of the IST. Solutions of the MKdV equation are mapped by an explicit nonlinear transformation known as the 'Miura transformation' into solutions of the KdV equation. Historically, the Miura transformation manifested the intimate connection between solutions of the KdV equation and the inverse problem for the one-dimensional time independent Schroedinger equation. In light of the MKdV equation's significance, it is natural to seek 'modified' versions of the ILW and BO equations. Solutions of each modified nonlinear singular integro-differential equation should be mapped by an analogue of the original Miura transformation into solutions of the 'unmodified' equation. In parallel with the limiting cases of the ILW equation, the modified version of the ILW equation should reduce to the MKdV equation in the shallow water limit and to the modified version of the BO equation in the deep water limit. The Modified Intermediate Long Wave (MILW) and Modified Benjamin-Ono (MBO) equations are the two nonlinear singular integro-differential equations that display all the required attributes. Several researchers have shown that the MILW and MBO equations exhibit the signature characteristic of soliton equations. Despite the significance of the MILW and MBO equations to soliton theory, and the possible physical applications of the MILW and MBO equations, the initial value problems for these equations have not been solved. In this thesis we use the IST to solve the initial value problems for the MILW and MBO equations on the real-line. The only restrictions that we place on the initial values for the MILW and MBO equations are that they be real-valued, sufficiently smooth and decay to zero as the absolute value of the spatial variable approaches large values.
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Circularly symmetric iris in coaxial waveguideNabulsi, Khalid Ali January 1980 (has links)
No description available.
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An Application of the Inverse Scattering Transform to some Nonlinear Singular Integro-Differential Equations.Scoufis, George January 1999 (has links)
ABSTRACT The quest to model wave propagation in various physical systems has produced a large set of diverse nonlinear equations. Nonlinear singular integro-differential equations rank amongst the intricate nonlinear wave equations available to study the classical problem of wave propagation in physical systems. Integro-differential equations are characterized by the simultaneous presence of integration and differentiation in a single equation. Substantial interest exists in nonlinear wave equations that are amenable to the Inverse Scattering Transform (IST). The IST is an adroit mathematical technique that delivers analytical solutions of a certain type of nonlinear equation: soliton equation. Initial value problems of numerous physically significant nonlinear equations have now been solved through elegant and novel implementations of the IST. The prototype nonlinear singular integro-differential equation receptive to the IST is the Intermediate Long Wave (ILW) equation, which models one-dimensional weakly nonlinear internal wave propagation in a density stratified fluid of finite total depth. In the deep water limit the ILW equation bifurcates into a physically significant nonlinear singular integro-differential equation known as the 'Benjamin-Ono' (BO) equation; the shallow water limit of the ILW equation is the famous Korteweg-de Vries (KdV) equation. Both the KdV and BO equations have been solved by dissimilar implementations of the IST. The Modified Korteweg-de Vries (MKdV) equation is a nonlinear partial differential equation, which was significant in the historical development of the IST. Solutions of the MKdV equation are mapped by an explicit nonlinear transformation known as the 'Miura transformation' into solutions of the KdV equation. Historically, the Miura transformation manifested the intimate connection between solutions of the KdV equation and the inverse problem for the one-dimensional time independent Schroedinger equation. In light of the MKdV equation's significance, it is natural to seek 'modified' versions of the ILW and BO equations. Solutions of each modified nonlinear singular integro-differential equation should be mapped by an analogue of the original Miura transformation into solutions of the 'unmodified' equation. In parallel with the limiting cases of the ILW equation, the modified version of the ILW equation should reduce to the MKdV equation in the shallow water limit and to the modified version of the BO equation in the deep water limit. The Modified Intermediate Long Wave (MILW) and Modified Benjamin-Ono (MBO) equations are the two nonlinear singular integro-differential equations that display all the required attributes. Several researchers have shown that the MILW and MBO equations exhibit the signature characteristic of soliton equations. Despite the significance of the MILW and MBO equations to soliton theory, and the possible physical applications of the MILW and MBO equations, the initial value problems for these equations have not been solved. In this thesis we use the IST to solve the initial value problems for the MILW and MBO equations on the real-line. The only restrictions that we place on the initial values for the MILW and MBO equations are that they be real-valued, sufficiently smooth and decay to zero as the absolute value of the spatial variable approaches large values.
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An application of the inverse scattering transform to some nonlnear singular integro-differential equationsScoufis, George. January 1999 (has links)
Thesis (Ph. D.)--University of Sydney, 1999. / Title from title screen (viewed Apr. 21, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliography. Also available in print form.
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Nichtlineare Integro-Differential-Gleichungen zur Modellierung interaktiver Musterbildungsprozesse auf S¹Geigant, Edith. January 1999 (has links)
Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1999. / Includes bibliographical references (p. 203-205).
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Integro-differential-equation models in ecology and epidemiology /Medlock, Jan P., January 2004 (has links)
Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 73-77).
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Numerical analysis of delay differential and integro-differential equations /Zhang, Wenkui, January 1998 (has links)
Thesis (Ph.D.)--Memorial University of Newfoundland, 1999. / Bibliography: leaves 121-135.
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Uma teoria de periodicidade para certas equações de evoluçãoLuis de Andrade Santos, Bruno 31 January 2010 (has links)
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arquivo647_1.pdf: 897384 bytes, checksum: c9418f10abbbb7ccd442ab4b1654fa38 (MD5)
license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5)
Previous issue date: 2010 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho estudamos diversos tipos de periodicidade para equações de evolução. As
técnicas utilizadas são uma combinação de Análise Funcional e Topologia. Para exibir a
aplicabilidade de nossos resultados vários exemplos são apresentados. A saber, mostramos
aplicações em equações diferenciais parciais, equações diferenciais fracionárias e equações
integrais com retardo infinito
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Continuum Models for the Spread of Alcohol AbuseTeymuroglu, Zeynep 23 September 2008 (has links)
No description available.
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