Anatoly NIKITIN
Department of Applied Research,
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv-4, UKRAINE
E-mail: nikitin@imath.kiev.ua

Solitary wave and other solutions for nonlinear heat equations

Abstract:
New exact solutions for the heat equation with the third-order polynomial non-linearity and for the Fisher equation are found. The non-linear heat equations admitting soliton solutions are found. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.