Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations
Abstract
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type (R. Cherniha J. Phys. A: Math. Theor., 2010. vol. 43., 405207), an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The form-preserving transformations for this class of systems are constructed and it is shown that this list contains only non-equivalent systems. The obtained symmetries permit to reduce the reaction-diffusion systems under study to two-dimensional systems of ordinary differential equations and to find exact solutions. As a non-trivial example, multiparameter families of exact solutions are explicitly constructed for two nonlinear reaction-diffusion systems. A possible interpretation to a biologically motivated model is presented.
Cite
@article{arxiv.1304.6595,
title = {Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations},
author = {Roman Cherniha and Vasyl' Davydovych},
journal= {arXiv preprint arXiv:1304.6595},
year = {2019}
}