Numerical simulation of a nonlinear wave equation and recurrence of initial states

In 1955 Fermi, Pasta and Ulam (FPU) [7] observed an unusual recurrence to initial state in numerical solutions of a nonlinear wave equation. Zabusky and Kruskal (ZK) [47] have subsequently found an explanation for this phenomenon based on special travelling wave solutions ("solitons") of t...

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Main Author: Buckley, Albert Grant
Language:English
Published: University of British Columbia 2011
Online Access:http://hdl.handle.net/2429/31823
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spelling ndltd-UBC-oai-circle.library.ubc.ca-2429-318232018-01-05T17:46:16Z Numerical simulation of a nonlinear wave equation and recurrence of initial states Buckley, Albert Grant In 1955 Fermi, Pasta and Ulam (FPU) [7] observed an unusual recurrence to initial state in numerical solutions of a nonlinear wave equation. Zabusky and Kruskal (ZK) [47] have subsequently found an explanation for this phenomenon based on special travelling wave solutions ("solitons") of the (nonlinear) Korteweg de Vries (KdV) equation. In this thesis we extend ZK's explanation to a similar nonlinear wave equation given by Johnson[14]. We investigate existence and uniqueness of solitons for a (nonlinear) generalization of the KdV equation. (Chapter II) and present computational results to illustrate ZK's soliton explanation of the recurrence, both for FPU's equation and Johnson's equation (Chapter III). In Chapter IV we give some results concerning the stability of the difference schemes used to obtain solutions to the nonlinear partial differential equations. Science, Faculty of Mathematics, Department of Graduate 2011-02-25T20:54:57Z 2011-02-25T20:54:57Z 1972 Text Thesis/Dissertation http://hdl.handle.net/2429/31823 eng For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. University of British Columbia
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language English
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description In 1955 Fermi, Pasta and Ulam (FPU) [7] observed an unusual recurrence to initial state in numerical solutions of a nonlinear wave equation. Zabusky and Kruskal (ZK) [47] have subsequently found an explanation for this phenomenon based on special travelling wave solutions ("solitons") of the (nonlinear) Korteweg de Vries (KdV) equation. In this thesis we extend ZK's explanation to a similar nonlinear wave equation given by Johnson[14]. We investigate existence and uniqueness of solitons for a (nonlinear) generalization of the KdV equation. (Chapter II) and present computational results to illustrate ZK's soliton explanation of the recurrence, both for FPU's equation and Johnson's equation (Chapter III). In Chapter IV we give some results concerning the stability of the difference schemes used to obtain solutions to the nonlinear partial differential equations. === Science, Faculty of === Mathematics, Department of === Graduate
author Buckley, Albert Grant
spellingShingle Buckley, Albert Grant
Numerical simulation of a nonlinear wave equation and recurrence of initial states
author_facet Buckley, Albert Grant
author_sort Buckley, Albert Grant
title Numerical simulation of a nonlinear wave equation and recurrence of initial states
title_short Numerical simulation of a nonlinear wave equation and recurrence of initial states
title_full Numerical simulation of a nonlinear wave equation and recurrence of initial states
title_fullStr Numerical simulation of a nonlinear wave equation and recurrence of initial states
title_full_unstemmed Numerical simulation of a nonlinear wave equation and recurrence of initial states
title_sort numerical simulation of a nonlinear wave equation and recurrence of initial states
publisher University of British Columbia
publishDate 2011
url http://hdl.handle.net/2429/31823
work_keys_str_mv AT buckleyalbertgrant numericalsimulationofanonlinearwaveequationandrecurrenceofinitialstates
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