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.

Conservation Laws and Exact Solutions with Symmetry Reduction of Nonlinear Reaction Diffusion Equations

2015 ◽  
Vol 16 (3-4) ◽  
pp. 191-196 ◽  
Author(s):  
Filiz Tascan ◽  
Arzu Yakut
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Lie Point Symmetries ◽  
Important Place ◽  
Physical Problems ◽  
Nonlinear Reaction

AbstractIn this work we study one of the most important applications of symmetries to physical problems, namely the construction of conservation laws. Conservation laws have important place for applications of differential equations and solutions, also in all physics applications. And so, this study deals conservation laws of first- and second-type nonlinear (NL) reaction diffusion equations. We used Ibragimov’s approach for finding conservation laws for these equations. And then, we found exact solutions of first- and second-type NL reaction diffusion equations with Lie-point symmetries.

Sign in / Sign up

Export Citation Format

Share Document