Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khokhlov equation

F. Güngör*, C. Özemir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 languageEnglish
Pages (from-to)623-638
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.


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


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