scholarly journals Strong \begin{document}$ (L^2,L^\gamma\cap H_0^1) $\end{document}-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension

2020 ◽  
Vol 28 (3) ◽  
pp. 1357-1374 ◽  
Author(s):  
Hongyong Cui ◽  
◽  
Peter E. Kloeden ◽  
Wenqiang Zhao ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Diffusion Equation ◽  
Space Dimension ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation

scholarly journals Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (G′/G)-Expansion Method

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Expansion Method ◽  
Reaction Diffusion Equation ◽  
Wave Solutions ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation ◽  
Constant Coefficients

We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.

1-Soliton Solution of the Nonlinear Reaction-Diffusion Equation

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Anjan Biswas
Keyword(s):  
Solitary Wave ◽  
Diffusion Equation ◽  
Soliton Solution ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Nonlinear Reaction ◽  
Nonlinear Reaction Diffusion Equation

In this paper, the 1-soliton solution of the nonlinear reaction-diffusion equation is obtained. The solitary wave ansatz is employed to obtain the solution.

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