Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation

Autor:	Gungor, F., Ozemir, C.
Rok vydání:	2014
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems
Zdroj:	J. Math. Anal. and Appl., 423, 623 - 638 (2015)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1402.1941 Zobrazit plný text záznamu View this record from Arxiv