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Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations

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Abstract

An efficient method for finding operators of conditional symmetry, which form a basis of the Galilean algebra, is suggested for a class of Galilei noninvariant parabolic equations. Additional conditions, under which the symmetry can be extended, are described. For the nonlinear equation under consideration, the antireduction is realized and some exact solutions are found by using the conditional Galilei invariance of its differential consequences.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. I. Fushchich (Corresponding Member, Ukrainian Academy of Sciences) & V. I. Chopik

Authors
  1. V. I. Fushchich
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  2. V. I. Chopik
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1433–1443, October, 1993.

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Fushchich, V.I., Chopik, V.I. Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations. Ukr Math J 45, 1609–1622 (1993). https://doi.org/10.1007/BF01571094

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  • DOI: https://doi.org/10.1007/BF01571094

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