Solutions of Fisher and Burger's equations with finite transport memory

Details Solutions of Fisher and Burger's equations with finite transport memory Solutions of Fisher and Burger's equations with finite transport memory

2001-12-18

arxiv.org/abs/nlin/0112025v2

Nonlinear Sciences

Pattern Formation and Solitons

6 pages, 2 figures, RevTex4

Scientific paper

The Fisher and Burgers' equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the traveling wavefront is dependent on the relaxation time in Fisher equation, memory effects significantly smoothen out the shock wave nature of Burgers' solution, without making any influence on the corresponding wave speed. We numerically analyze the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow travelling wave solution to exist for appreciable finite memory effect.

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