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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.

MSC:
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
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