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The Davey-Stewartson equations : a numerical study

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dc.contributor.advisor Weideman, Andre
dc.creator White, Peter W.
dc.date.accessioned 2010-07-16T20:16:38Z
dc.date.available 2010-07-16T20:16:38Z
dc.date.issued 1994-06-29
dc.identifier.uri http://hdl.handle.net/1957/16812
dc.description Graduation date: 1995 en
dc.description.abstract In 1974 Davey and Stewartson used a multi-scale analysis to derive a coupled system of nonlinear partial differential equations which describes the evolution of a three dimensional wave packet in water of a finite depth. This system of equations is the closest integrable two dimensional analog of the well-known one dimensional nonlinear Schrodinger equation. The method of inverse scattering can thus be used to solve the Davey-Stewartson equations in theory, but in practice this method is not feasible with arbitrary initial conditions. In this thesis we present a numerical method for solving the Davey-Stewartson equations. It is an extension of the split-step Fourier method that proved to be so successful for the nonlinear Schrodinger equation. This method is tested on some known soliton and dromion solutions and then used to study modulational instability and solutions which become singular in finite time. en
dc.language.iso en_US en
dc.subject.lcsh Differential equations, Nonlinear -- Numerical solutions en
dc.title The Davey-Stewartson equations : a numerical study en
dc.type Thesis/Dissertation en
dc.degree.name Doctor of Philosophy (Ph. D.) in Mathematics en
dc.degree.level Doctoral en
dc.degree.discipline Science en
dc.degree.grantor Oregon State University en
dc.description.digitization File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR. en

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