TY - JOUR
T1 - Traveling waves in a reaction-diffusion system
T2 - Diffusion with finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics
AU - Fedotov, Sergei
PY - 1998/1/1
Y1 - 1998/1/1
N2 - An asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure, and the singular perturbation techniques involving the large deviations theory for the Poisson random walk. The exact formula for the position and speed of reaction front is derived. It is found that the reaction front dynamics is formally associated with the relativistic Hamiltonian/Lagrangian mechanics.
AB - An asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure, and the singular perturbation techniques involving the large deviations theory for the Poisson random walk. The exact formula for the position and speed of reaction front is derived. It is found that the reaction front dynamics is formally associated with the relativistic Hamiltonian/Lagrangian mechanics.
UR - http://www.scopus.com/inward/record.url?scp=0001185435&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.58.5143
DO - 10.1103/PhysRevE.58.5143
M3 - Article
AN - SCOPUS:0001185435
SN - 1063-651X
VL - 58
SP - 5143
EP - 5145
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 4
ER -