### Abstract

© 2015 IOP Publishing Ltd & London Mathematical Society. We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.

Original language | English |
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Pages (from-to) | 1597-1606 |

Journal | Nonlinearity |

Volume | 28 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Jun 2015 |

### Keywords

- algebraic invariant solution
- Fischer-Kolmogorov equation
- partial differential equation
- polynomial differential equation
- travelling wave

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## Cite this

Gasull, A., & Giacomini, H. (2015). Explicit travelling waves and invariant algebraic curves.

*Nonlinearity*,*28*(6), 1597-1606. https://doi.org/10.1088/0951-7715/28/6/1597