2000•SIAM Journal on Applied MathematicsRequires access

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

John J. Tyson, Pavel K. Brazhnik

Abstract

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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Key concepts: Fisher equation, Traveling wave, Curvature, Quadratic equation, Mathematics, Mathematical analysis, Plane (geometry), Dispersion (optics)