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Group Classifications, Symmetry Reductions and Exact Solutions to the Nonlinear Elastic Rod Equations

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Abstract

In this paper, the Lie symmetry analysis are performed on the three nonlinear elastic rod (NER) equations. The complete group classifications of the generalized nonlinear elastic rod equations are obtained. The symmetry reductions and exact solutions to the equations are presented. Furthermore, by means of dynamical system and power series methods, the exact explicit solutions to the equations are investigated. It is shown that the combination of Lie symmetry analysis and dynamical system method is a feasible approach to deal with symmetry reductions and exact solutions to nonlinear PDEs.

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Authors and Affiliations

  1. Department of Mathematics, Binzhou University, Binzhou, Shandong, 256603, China

    Hanze Liu

  2. Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan, 650093, China

    Jibin Li

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China

    Jibin Li

  4. The Center for Economic Research, Shandong University, Ji’nan, Shandong, 250100, China

    Lei Liu

Authors
  1. Hanze Liu
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  2. Jibin Li
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  3. Lei Liu
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Corresponding author

Correspondence to Hanze Liu.

Additional information

This work is supported by the Natural Science Foundation of China (No. 10971018), the Natural Science Foundation of Shandong Province (No. ZR2010AM029), the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province (No. BS2010SF001) and the Doctoral Foundation of Binzhou University (No. 2009Y01).

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Liu, H., Li, J. & Liu, L. Group Classifications, Symmetry Reductions and Exact Solutions to the Nonlinear Elastic Rod Equations. Adv. Appl. Clifford Algebras 22, 107–122 (2012). https://doi.org/10.1007/s00006-011-0290-8

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  • DOI: https://doi.org/10.1007/s00006-011-0290-8

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