广义Kuznetsov-Zabolotskaya-Khoklov方程的Lie对称性
Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation
摘要：
考虑了一类广义Kuznetsov-Zabolotskaya-Khokhlov（gKZK）方程，确定了它的等价群，并利用等价群给出了这类方程的完全对称分类.利用无穷维对称性将这类方程化为（1+1）维偏微分方程。特别注意一类广义无色散KP（gdKP）或Zabolotskaya-Khokhlov方程作为gKZK方程的子类的群论性质。给出了gdKP方程在含有维拉索罗代数的李代数下不变的条件.当且仅当这个方程是完全可积的。一个类似的连接，广义KP方程。
英文摘要：
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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