## Abstract

We construct Lax pairs for general

*d*+ 1 dimensional evolution equations in the form*u*=_{t}*F[u]*, where*F[u]*depends on the field*u*and its space derivatives. As an example we study a 3 + 1 dimensional integrable generalization of the Burgers equation. We develop a procedure to generate some exact solutions of this equation, based on a class of discrete symmetries of the Darboux transformation type. In the one-dimensional limit, these symmetries reduce to the Cole-Hopf substitution for the Burgers equation. It is discussed how the technique can be used to construct exact solutions for higher-dimensional evolution PDEs in a broader context.Translated title of the contribution | Lax pairs for higher-dimensional evolution PDEs and a 3+1 dimensional integrable generalization of the Burgers equation |
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Original language | English |

Pages (from-to) | 731 - 741 |

Journal | Proceedings of the American Mathematical Society |

Volume | 135 |

Issue number | 3 |

Publication status | Published - 2007 |

### Bibliographical note

Publisher: Amer Mathematical SocOther identifier: IDS number 108KI