Painlevé test, integrability, and exact solutions for density-dependent reaction–diffusion equations with polynomial reaction functions

2012 ◽  
Vol 219 (6) ◽  
pp. 3055-3064 ◽  
Author(s):  
Jessica Hearns ◽  
Robert A. Van Gorder ◽  
S. Roy Choudhury
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Painlevé Test ◽  
Density Dependent ◽  
Reaction Functions

scholarly journals Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PLoS ONE ◽  
2015 ◽  
Vol 10 (9) ◽  
pp. e0138894 ◽  
Author(s):  
Matthew J. Simpson ◽  
Jesse A. Sharp ◽  
Liam C. Morrow ◽  
Ruth E. Baker
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Growing Domain ◽  
Linear Reaction

scholarly journals Third-Order Conditional Lie–Bäcklund Symmetries of Nonlinear Reaction-Diffusion Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Keqin Su ◽  
Jie Cao
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Governing Equations ◽  
Third Order ◽  
Differential Constraints ◽  
The Third ◽  
Nonlinear Reaction

The third-order conditional Lie–Bäcklund symmetries of nonlinear reaction-diffusion equations are constructed due to the method of linear determining equations. As a consequence, the exact solutions of the resulting equations are derived due to the compatibility of the governing equations and the admitted differential constraints, which are resting on the characteristic of the admitted conditional Lie–Bäcklund symmetries to be zero.

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