%0 Journal Article %1 ablowitz1979explicit %A Ablowitz, Mark %A Zeppetella, Anthony %D 1979 %J Bulletin of Mathematical Biology %K Fisher-KPP explicit_solution travelling_wave %N 6 %P 835--840 %T Explicit solutions of Fisher's equation for a special wave speed %U http://dx.doi.org/10.1007/BF02462380 %V 41 %X The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds $$c = 5/(6) $$. In this case the equation is shown to be of Painlevé type, i.e. solutions admit only poles as movable singularities. The general solution for this wave speed is found and a method is presented that can be applied to the solution of other nonlinear equations of biological and physical interest.

@article{ablowitz1979explicit, abstract = {The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds $$c = \pm 5/\sqrt {(6)} $$. In this case the equation is shown to be of Painlevé type, i.e. solutions admit only poles as movable singularities. The general solution for this wave speed is found and a method is presented that can be applied to the solution of other nonlinear equations of biological and physical interest.}, added-at = {2010-03-29T00:01:55.000+0200}, author = {Ablowitz, Mark and Zeppetella, Anthony}, biburl = {https://www.bibsonomy.org/bibtex/235ec63dde4f092f47cc60288a6cc26e7/peter.ralph}, interhash = {a0a44777fe0989262676af741a6b42ae}, intrahash = {35ec63dde4f092f47cc60288a6cc26e7}, journal = {Bulletin of Mathematical Biology}, keywords = {Fisher-KPP explicit_solution travelling_wave}, month = nov, number = 6, pages = {835--840}, timestamp = {2014-03-10T22:48:32.000+0100}, title = {Explicit solutions of Fisher's equation for a special wave speed}, url = {http://dx.doi.org/10.1007/BF02462380}, volume = 41, year = 1979 }