Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity
Abstract
:1. Introduction
2. Basic Notations and Theorems
3. Equation (3) Admitting CLBS (1) and H–J SI (2)
- For ,
- For ,
- For ,
4. Symmetry Reductions of Equation (3)
- For ,
- For ,The solutions of this system of ODEs with are listed below:
- For ,
- For ,The solutions blow up along the curves when and extinguish along the curves when .
- For ,
- (i)
- For and ,
- (ii)
- For ,
- (iii)
- For ,
- For ,The solutions blow up along the curves when and extinguish along the curves when .
- For ,
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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1 | 2 | 1 | |||||
2 | 2 | 3 | |||||
3 | 2 | 3 | |||||
4 | 2 | ||||||
5 | 2 | 6 | 0 | ||||
6 | 0 | ||||||
7 | 0 | ||||||
8 | 2 | 0 | |||||
9 | 0 | ||||||
10 | 0 | ||||||
11 | 0 |
No. | ||||
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1 | ||||
2 | ||||
3 | ||||
4 |
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Ji, L.; Feng, W. Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity. Symmetry 2018, 10, 267. https://doi.org/10.3390/sym10070267
Ji L, Feng W. Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity. Symmetry. 2018; 10(7):267. https://doi.org/10.3390/sym10070267
Chicago/Turabian StyleJi, Lina, and Wei Feng. 2018. "Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity" Symmetry 10, no. 7: 267. https://doi.org/10.3390/sym10070267