Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation

F. Gungor; C. Ozemir

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arXiv · 1402.1941

Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation

F. Gungor·C. Ozemir

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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.

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BibTeX RIS

F. Gungor, C. Ozemir. 2014-02-09. Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation. https://arxiv.org/abs/1402.1941

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