scholarly journals Conditional Lie-Bäcklund Symmetry Reductions and Exact Solutions of a Class of Reaction-Diffusion Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Xinyang Wang ◽  
Junquan Song
Keyword(s):  
Dynamical Systems ◽  
Exact Solutions ◽  
Separation Of Variables ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Financial Mathematics ◽  
Symmetry Reductions ◽  
Finite Dimensional ◽  
Wide Range

The method of conditional Lie-Bäcklund symmetry is applied to solve a class of reaction-diffusion equations ut+uxx+Qxux2+Pxu+Rx=0, which have wide range of applications in physics, engineering, chemistry, biology, and financial mathematics theory. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamical systems. The exact solutions obtained in concrete examples possess the extended forms of the separation of variables.

scholarly journals Wave pinning in strips

2006 ◽  
Vol 136 (5) ◽  
pp. 971-995 ◽  
Author(s):  
Karsten Matthies ◽  
C. E. Wayne
Keyword(s):  
Dynamical Systems ◽  
Parameter Space ◽  
Heterogeneous Media ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

We consider the existence of stationary or pinned waves of reaction–diffusion equations in heterogeneous media. By combining averaging, homogenization and dynamical-systems techniques we prove under mild non-degeneracy conditions that if the heterogeneity is periodic with period ε, pinned solutions persist at most for intervals in parameter space whose length is O(e−c/√ε).

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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