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

PDF

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

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