Painlevé Test, Generalized Symmetries, Bäcklund Transformations and Exact Solutions to the Third-Order Burgers’ Equations

In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other...

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Bibliographic Details
Published inJournal of statistical physics Vol. 158; no. 2; pp. 433 - 446
Main Author Liu, Hanze
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.01.2015
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
35C05
Generalized symmetry
Integrability
22E70
Bäcklund transformation
17B80
Third-order Burger’s equation
Exact solution
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Summary:In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers’ equation, the Painlevé property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation method. The Bäcklund Transformations of the equations are constructed based on the symmetries, respectively. Furthermore, the exact explicit solutions to the equations are investigated in terms of the symmetries, Bäcklund transformations and transformations of the equations.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-1130-8