Study of transients in the propagation of nonlinear waves in some reaction diffusion systems

@article{Giuggioli2006StudyOT,
  title={Study of transients in the propagation of nonlinear waves 
in some reaction diffusion systems},
  author={Luca Giuggioli and Ziya Kalay and V. M. Kenkre},
  journal={The European Physical Journal B},
  year={2006},
  volume={62},
  pages={341-348}
}
Abstract.We study the transient dynamics of single species reaction diffusion systems whose reaction terms f(u) vary nonlinearly near u ≈ 0, specifically as f(u) ≈ u2 and f(u) ≈ u3. We consider three cases, calculate their traveling wave fronts and speeds analytically and solve the equations numerically with different initial conditions to study the approach to the asymptotic front shape and speed. Observed time evolution is found to be quite sensitive to initial conditions and to display in… 
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