On Traveling Wave Solutions of Fisher's Equation in Two Spatial Dimensions

@article{Tyson2000OnTW,
  title={On Traveling Wave Solutions of Fisher's Equation in Two Spatial Dimensions},
  author={John J. Tyson and Pavel K. Brazhnik},
  journal={SIAM Journal of Applied Mathematics},
  year={2000},
  volume={60},
  pages={371-391}
}
It is shown for the quadratic Fisher equation in two spatial dimensions that, along with a plane wave, there exist several other traveling waves with nontrivial front geometry. Some of the solutions are found in explicit form; others are constructed approximately. The dispersion relationship and velocity-curvature dependence generated by these solutions are studied. 

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Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem

  • A. N. Kolmogorov, I. G. Petrovsky, N. S. Piskunov
  • Dynamics of Curved Fronts, P. Pelcé, ed…
  • 1988
Highly Influential
2 Excerpts

Eikonal relation in highly dispersive excitable media

  • A. M. Pertsov, M. Wellner, J. Jalife
  • Phys. Rev. Lett., 78
  • 1997
1 Excerpt

Exact solutions for the kinematic model of autowaves in two-dimensional media

  • P. K. Brazhnik
  • Phys. D, 94
  • 1996
2 Excerpts

On travelling waves and double-periodic structures in two-dimensional sine- Gordon systems

  • N. K. Vitanov
  • J. Phys. A: Math. Gen., 29
  • 1996
1 Excerpt

Non-spiral autowave structures in unrestricted excitable media

  • P. K. Brazhnik, V. A. Davydov
  • Phys. Lett. A, 199
  • 1995
2 Excerpts

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