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Finite symmetry transformation groups and exact solutions of the cylindrical Korteweg-de Vries equation

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  • Ye, Wang-Chuan
  • Li, Biao

Abstract

Based on the new symmetry group method developed by Lou et al. and symbolic computation, both the Lie point groups and the non-Lie symmetry groups of the cylindrical Korteweg-de Vries (cKdV) equation are obtained. With the transformation groups, a type of group invariant solutions of cKdV equation can be derived from a simple one. Furthermore, some transformations from the cKdV equation to KP equation can also be discovered by this method.

Suggested Citation

  • Ye, Wang-Chuan & Li, Biao, 2009. "Finite symmetry transformation groups and exact solutions of the cylindrical Korteweg-de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2623-2628.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2623-2628
    DOI: 10.1016/j.chaos.2009.03.186
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    References listed on IDEAS

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    1. Syam, Muhammed I. & Khashan, Hani A. & Al-Mdallal, Qasem M., 2008. "Nonlinear eigenvalue problems with symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 931-941.
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    5. He, Ji-Huan & Xu, Lan, 2009. "Number of elementary particles using exceptional Lie symmetry groups hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2119-2124.
    6. Ma, Wen-Xiu & Chen, Min, 2007. "Do symmetry constraints yield exact solutions?," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1513-1517.
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