## Abstract

We consider a class of generalized Kuznetsov-Zabolotskaya-Khokhlov (gKZK) equations and determine its equivalence group, which is then used to give a complete symmetry classification of this class. The infinite-dimensional symmetry is used to reduce such equations to (1. +. 1)-dimensional PDEs. Special attention is paid to group-theoretical properties of a class of generalized dispersionless KP (gdKP) or Zabolotskaya-Khokhlov equations as a subclass of gKZK equations. The conditions are determined under which a gdKP equation is invariant under a Lie algebra containing the Virasoro algebra as a subalgebra. This occurs if and only if this equation is completely integrable. A similar connection is shown to hold for generalized KP equations.

Original language | English |
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Pages (from-to) | 623-638 |

Number of pages | 16 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 423 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

### Bibliographical note

Publisher Copyright:© 2014 Elsevier Inc.

## Keywords

- Classification
- Equivalence group
- Generalized Kuznetsov-Zabolotskaya-Khokhlov equations
- Generalized dKP and KP equations
- Symmetry