Multiple singular manifold method and extended direct method: Application to the Burgers equation

DOI10.1007/BF02435927zbMath0884.35139OpenAlexW2314079643MaRDI QIDQ1367645

Qu Changzheng

Publication date: 25 September 1997

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02435927

zbMATH Keywords

Burgers equationBäcklund transformationssimilarity reductionsextended direct methodmultiple singular manifold method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Cites Work

• Unnamed Item
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• The Painlevé property for partial differential equations
• On classes of integrable systems and the Painlevé property
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• Nonclassical symmetry solutions and the methods of Bluman–Cole and Clarkson–Kruskal
• Nonlinear interaction of traveling waves of nonintegrable equations
• New exact solutions of Burgers’s equation—an extension to the direct method of Clarkson and Kruskal
• Modified singular manifold expansion: application to the Boussinesq and Mikhailov-Shabat systems
• The partial differential equation u_t + uu_x = μ_xx

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