The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. (English) Zbl 1119.65100

Summary: 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, 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.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
Full Text: DOI


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