scholarly journals Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 267
Author(s):  
Lina Ji ◽  
Wei Feng
Keyword(s):  
Reaction Diffusion ◽  
Second Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Differential Constraints ◽  
Nonlinear 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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