A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.
@article{bwmeta1.element.doi-10_2478_BF02475981,
author = {Anatoly Nikitin and Tetyana Barannyk},
title = {Solitary wave and other solutions for nonlinear heat equations},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {840-858},
zbl = {1116.35035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475981}
}
Anatoly Nikitin; Tetyana Barannyk. Solitary wave and other solutions for nonlinear heat equations. Open Mathematics, Tome 2 (2004) pp. 840-858. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475981/
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