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Conditional Lie‐Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source

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  • Junquan Song
  • Yujian Ye
  • Danda Zhang
  • Jun Zhang

Abstract

Conditional Lie‐Bäcklund symmetry approach is used to study the invariant subspace of the nonlinear diffusion equations with source ut=e−qx(epxP(u)uxm)x+Q(x,u), m ≠ 1. We obtain a complete list of canonical forms for such equations admit multidimensional invariant subspaces determined by higher order conditional Lie‐Bäcklund symmetries. The resulting equations are either solved exactly or reduced to some finite‐dimensional dynamic systems.

Suggested Citation

  • Junquan Song & Yujian Ye & Danda Zhang & Jun Zhang, 2014. "Conditional Lie‐Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:898032
    DOI: 10.1155/2014/898032
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    References listed on IDEAS

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    1. Sophocleous, Christodoulos, 2003. "Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 169-183.
    2. Sophocleous, Christodoulos, 2005. "Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(3), pages 457-471.
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