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Nonclassical potential symmetries and invariant solutions of heat equation

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Abstract

Some nonclassical potential symmetry generators and group-invariant solutions of heat equation and wave equation were determined. It is shown that some new explicit solutions of partial differential equations in conserved form can be constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot be obtained by using the Lie or Lie-Bäcklund symmetry group generators of differential equations.

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Authors and Affiliations

  1. School of Science, Chongqing Technology and Business University, Chongqing, 400067, P. R. China

    Qin Mao-chang  (秦茂昌) (Doctor)

  2. School of Science, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Qin Mao-chang  (秦茂昌) (Doctor), Mei Feng-xiang  (梅凤翔) & Xu Xue-jun  (许学军)

Authors
  1. Qin Mao-chang  (秦茂昌)
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  2. Mei Feng-xiang  (梅凤翔)
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  3. Xu Xue-jun  (许学军)
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Corresponding author

Correspondence to Qin Mao-chang  (秦茂昌).

Additional information

Project supported by the National Natural Sciences Foundation of China (No.10272021) and the Doctoral Program Foundation of Education Ministry of China (No.20040007022)

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Qin, Mc., Mei, Fx. & Xu, Xj. Nonclassical potential symmetries and invariant solutions of heat equation. Appl Math Mech 27, 241–246 (2006). https://doi.org/10.1007/s10483-006-0213-y

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  • DOI: https://doi.org/10.1007/s10483-006-0213-y

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