The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations

The tanh–coth method is used to derive solitons and kink solutions for some of the well-known nonlinear parabolic partial differential equations. The equations include the Fisher equation, Newell–Whithead equation, Allen–Cahn equation, FitzHugh–Nagumo equation, Fisher’s equation, and the Burgers–Fisher equation. The new tanh–coth approach provides abundant solitons and kink solutions in addition to the existing ones. The power of this manageable method is confirmed.