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Conditional Lie–Bäcklund symmetries and solutions of inhomogeneous nonlinear diffusion equations

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  • Ji, Lina

Abstract

The second-order conditional Lie–Bäcklund symmetries of nonlinear diffusion equations with variable coefficients are studied. A number of examples are considered and some exact solutions are constructed via the compatibility of conditional Lie–Bäcklund symmetries and the governing equations. These solutions possess the extended forms of the separation of variables, including the extensions of the instantaneous source solutions of the porous medium equations.

Suggested Citation

  • Ji, Lina, 2010. "Conditional Lie–Bäcklund symmetries and solutions of inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5655-5661.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5655-5661
    DOI: 10.1016/j.physa.2010.08.056
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    References listed on IDEAS

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    1. Gandarias, M.L., 2008. "New potential symmetries for some evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(10), pages 2234-2242.
    2. Sophocleous, Christodoulos, 2003. "Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 509-529.
    3. 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.
    4. Khater, A.H. & Moussa, M.H.M. & Abdul-Aziz, S.F., 2002. "Potential symmetries and invariant solutions for the inhomogeneous nonlinear diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 99-108.
    5. 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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    Cited by:

    1. Feng, Wei & Ji, Lina, 2013. "Conditional Lie–Bäcklund symmetries and functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 618-627.

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    5. Sophocleous, Christodoulos, 2003. "Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 509-529.
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