Nonlinear reaction-diffusion systems with a non-constant diffusivity: conditional symmetries in no-go case
arXiv:1609.09613 · doi:10.1016/j.amc.2015.06.017
Abstract
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.
arXiv admin note: text overlap with arXiv:1609.09607