Integrability characteristics of higher order nonlinear PDES using regular and invariant Painleve analysis
Keywords
Painleve equations, Painlevé analysis (invariant and regular), Lax pairs, Multisoliton solutions, Third-order dispersive evolution equations (u1 = uxxx + F(u, ux, uxx)), Fifth-order evolution equations (u1 = uxxxxx + G(u, uxx, uxxx))
Abstract
A mix of Invariant and Regular Painleve Analysis is employed to derive Lax Pairs and multisoliton solutions of various integrable members of the family of equations u1 = uxxx + F(u, ux , uxx ). The algorithmic nature of the procedure will be stressed, and the relative advantages of the two different formulations of the Painleve Analysis for different parts of the overall calculation will also be described. Possible applications to integrable members of the family u1 = uxxxxx + G(u, ux , uxx , uxxx ' ux.TXX ) will be touched upon.
Notes
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Graduation Date
2003
Advisor
Choudhury, S. Roy
Degree
Master of Science (M.S.)
College
College of Arts and Sciences
Department
Mathematics
Format
Pages
57 pages
Language
English
Length of Campus-only Access
None
Access Status
Masters Thesis (Open Access)
Identifier
DP0029085
Subjects
Arts and Sciences -- Dissertations; Academic; Dissertations; Academic -- Arts and Sciences; Painlevé equations; Differential equations, Nonlinear; Nonlinear partial differential operators; Nonlinear wave equations; Nonlinear waves--Mathematics
STARS Citation
Al Ghassani, Asma, "Integrability characteristics of higher order nonlinear PDES using regular and invariant Painleve analysis" (2003). Retrospective Theses and Dissertations. 732.
https://stars.library.ucf.edu/rtd/732
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