### Abstract

This is an extension of earlier work (SIAM J. Math. Anal. vol.16, p.221, 1985) by the authors which gives a correspondence between Lie symmetry operators (with non-trivial time dependence) for a given evolution equation and those evolution equations related to the given one by a change of independent and dependent coordinates. They work out the correspondence between symmetries of a system of evolution equations nu _{t}=K(y, v) and those systems u _{s}=J(x, u) related to it by a change of coordinates t=T(s, x, u), y=Y(s, x, u), v=V(s, x, u) and show (extending ideas of Humi (1986) and Rosencrans (1976)) how to determine the related equations directly from the symmetry operators without solving a system of differential equations. In general there are multiple evolution equations associated with a given symmetry; for the case of scalar evolution equations they compute explicitly the structure of each equivalence class.

Original language | English (US) |
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Article number | 018 |

Pages (from-to) | 5435-5446 |

Number of pages | 12 |

Journal | Journal of Physics A: General Physics |

Volume | 20 |

Issue number | 16 |

DOIs | |

State | Published - Dec 1 1987 |

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## Cite this

*Journal of Physics A: General Physics*,

*20*(16), 5435-5446. [018]. https://doi.org/10.1088/0305-4470/20/16/018