A supersymmetric extension of a two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this superalgebra into 63 equivalence classes is performed. For some of the subalgebras, it is found that the invariants have a non-standard structure. For six selected subalgebras, the symmetry reduction method is used to find invariants, orbits of the subgroups and reduced systems. Through the solutions of the reduced systems, the most general solutions are expressed in terms of arbitrary functions of one or two fermionic and one bosonic variables.

中文翻译：

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两相流系统超对称形式的不变解

制定了两相流体流动系统的超对称扩展。计算了该系统超对称扩展的Lie对称性的超代数。将该超级代数的一维子代数分类为63个等价类。对于某些子代数，发现不变量具有非标准结构。对于六个选定的子代数，使用对称约简方法查找子群的不变式，轨道和约简系统。通过简化系统的解，最一般的解用一个或两个铁离子变量和一个玻色子变量的任意函数表示。