Existence of traveling wave solutions for a reaction–diffusion equation with distributed delays

2007 ◽  
Vol 67 (8) ◽  
pp. 2415-2423 ◽  
Author(s):  
Yahong Peng ◽  
Yongli Song
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Distributed Delays ◽  
Reaction Diffusion Equation ◽  
Wave Solutions

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.

scholarly journals Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1999
Author(s):  
Hongpeng Guo ◽  
Zhiming Guo
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Local Reaction ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Birth Function ◽  
Wave Solutions ◽  
Monotonicity Assumption ◽  
Non Local

This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c>c*, where c*>0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

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