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Nonlinear evolution equations and optimization problems in Banach spacesLee, Haewon. January 2005 (has links)
Thesis (Ph.D.)--Ohio University, August, 2005. / Title from PDF t.p. Includes bibliographical references (p. 79-93)
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Forced Brakke flowsGraham, David(David Warwick),1976- January 2003 (has links)
For thesis abstract select View Thesis Title, Contents and Abstract
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Forced Brakke flowsGraham, David (David Warwick), 1976- January 2003 (has links)
Abstract not available
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Time series forecasting for non-static environments the dyfor genetic program model /Wagner, Neal FitzGerald. January 1900 (has links) (PDF)
Thesis (Ph.D.)--University of North Carolina at Charlotte, 2005. / Includes bibliographical references (leaves 71-79).
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The theory of integrated empathiesBrown, Thomas John. January 2005 (has links)
Thesis (PhD.(Mathematics))-University of Pretoria, 2005. / Includes bibliographical references. Available on the Internet via the World Wide Web.
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On the Cauchy problem for the linearized GPKdV and gauge transformations for a quadratic pencil and AKNS systemYordanov, Russi Georgiev 06 June 2008 (has links)
The present work in the area of soliton theory studies two problems which arise when seeking analytic solutions to certain nonlinear partial differential equations.
In the first one, Lax pairs associated with prolonged eigenfunctions and prolonged squared eigenfunctions (prolonged squares) are derived for a Schrödinger equation with a potential depending polynomially on the spectral parameter (of degree N) and its respective hierarchy of nonlinear evolution equations (here named generalized polynomial Korteweg-de Vries equations or GPKdV).
It is shown that the prolonged squares satisfy the linearized GPKdV equations. On that basis, the Cauchy problem for the linearized GPKdV has been solved by finding a complete set of such prolonged squares and applying an expansion formula derived in another work by the author.
The results are a generalization of the ones by Sachs (SIAM J. Math. Anal. 14, 1983, 674-683).
Moreover, a condition on the so-called recursion operator A is derived which generates the whole hierarchy of Lax pairs associated with the prolonged squares.
As for the second part of the work, it developed a scheme for deriving gauge transformations between different linear spectral problems. Then the scheme is applied to obtain all known Darboux transformations for a quadratic pencil (the spectral problem considered in the first part at N = 2), Schrödinger equation (N = 1), Ablowitz-Kaup-Newell-Segur (AKNS) system and also derive the Jaulent-Miodek transformation. Moreover, the scheme yields a large family of new transformations of the above types. It also gives some insight on the structure of the transformations and emphasizes the symmetry with respect to inversion that they possess. / Ph. D.
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