Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SYMMETRY REDUCTIONS, VARIABLE TRANSFORMATIONS AND EXACT SOLUTIONS TO THE SECOND-ORDER PDES

  • Liu, Hanze (Department of Mathematics, Binzhou University) ;
  • Liu, Lei (The Center for Economic Research, Shandong University)
  • Received : 2010.06.10
  • Accepted : 2010.09.08
  • Published : 2011.05.30
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Abstract

In this paper, the Lie symmetry analysis is performed on the three mixed second-order PDEs, which arise in fluid dynamics, nonlinear wave theory and plasma physics, etc. The symmetries and similarity reductions of the equations are obtained, and the exact solutions to the equations are investigated by the dynamical system and power series methods. Then, the exact solutions to the general types of PDEs are considered through a variable transformation. At last, the symmetry and integration method is employed for reducing the nonlinear ODEs.

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References

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