## Abstract

We investigate the existence of a one-parameter group of contact transformations for evolution-type equations u_{t} = F(t, x, u, u_{x}, u_{xx}, . . . , u_{(n)}) (subscripts denote differentiation unless otherwise indicated), where u_{(n)} is the nth derivative of u with respect to x. We prove that contact transformations of evolution equations, where F is expandable as a power series in terms of all derivatives of order higher than one, are just extended Lie point transformations. This result is extended to the case with m independent space variables. As a consequence, we obtain an ansatz for determining Lie point transformations for nth-order evolution equations with m independent space variables. Examples are given to verify the results obtained as well as to show how Lie point transformations of these evolution-type partial differential equations can be calculated from this ansatz.

Original language | English |
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Pages (from-to) | 8721-8730 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 32 |

Issue number | 49 |

DOIs | |

Publication status | Published - 10 Dec 1999 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy