标题： 非线性反应-扩散系统具有非常数扩散率：无解情况下的条件对称性 显示英文标题

标题： Nonlinear reaction-diffusion systems with a non-constant diffusivity: conditional symmetries in no-go case

摘要： Q-条件对称性（非经典对称性）对于具有非恒定扩散率的一类一般双组分反应-扩散系统进行了研究。这项工作是我们论文（Cherniha和Davydovych，2012）的自然延续，旨在扩展所谓的无解情况的结果。使用第一类Q-条件对称性的概念，得出了一类可接受此类对称性的反应-扩散系统的完整列表。获得的结果与之前得出的结果进行了比较。应用这些对称性将反应-扩散系统约化为二维动力系统（常微分方程系统）并寻找精确解。结果，构建了具有任意幂律扩散率的非线性反应-扩散系统的显式形式的多参数精确解族，并确定了它们在可能应用中的性质。 显示英文摘要

摘要： Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. The work is a natural continuation of our paper (Cherniha and Davydovych, 2012) in order to extend the results on so-called no-go case. Using the notion of Q-conditional symmetries of the first type, an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The results obtained are compared with those derived earlier. The symmetries for reducing reaction-diffusion systems to two-dimensional dynamical systems (ODE systems) and finding exact solutions are applied. As result, multiparameter families of exact solutions in the explicit form for nonlinear reaction-diffusion systems with an arbitrary power-law diffusivity are constructed and their properties for possible applicability are established.