Conditional symmetries and exact solutions of nonlinear reaction-diffusion systems with non-constant diffusivities
Abstract
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type, an exhausted list of reaction-diffusion systems admitting such symmetry is derived. The results obtained for the reaction-diffusion systems are compared with those for the scalar reaction-diffusion equations. The symmetries found for reducing reaction-diffusion systems to two-dimensional dynamical systems, i.e., ODE systems, and finding exact solutions are applied. As result, multiparameter families of exact solutions in the explicit form for a nonlinear reaction-diffusion system with an arbitrary diffusivity are constructed. Finally, the application of the exact solutions for solving a biologically and physically motivated system is presented.
Cite
@article{arxiv.1609.09607,
title = {Conditional symmetries and exact solutions of nonlinear reaction-diffusion systems with non-constant diffusivities},
author = {Roman Cherniha and Vasyl' Davydovych},
journal= {arXiv preprint arXiv:1609.09607},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1304.6595