International Journal of Theoretical Physics

, Volume 36, Issue 6, pp 1329–1339 | Cite as

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

  • Qu Changzheng
Article

Abstract

This paper considers the relationship between the multiple singular manifold method (MSMM) and the extended direct method (EDM) for studying partial differential equations. It is shown that the similarity reductions using EDM can be obtained by MSMM. The prototype example for illustrating the approach is the Burgers equation, which is the simplest evolution equation to embody nonlinearity and dissipation. As a conclusion of the MSMM, we obtain a set of Bäcklund transformations of the Burgers equation.

Keywords

Burger Equation Nonlinear PDEs Singular Manifold Backlund Transformation Conditional Symmetry 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Qu Changzheng
    • 1
  1. 1.Department of MathematicsNorthwest UniversityXi'anChina

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