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.

arXiv admin note: text overlap with arXiv:1304.6595

References in corpus (1)

• New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. I

Cited by in corpus (3)

• Nonlinear reaction-diffusion systems with a non-constant diffusivity: conditional symmetries in no-go case
• Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation
• Lie symmetries, reduction and exact solutions of the (1+2)-dimensional nonlinear problem