Periodic Wave Solution of the Generalized Burgers-Fisher Equation via Abelian Integral

In this paper, the global existence and uniqueness of an isolated periodic wave solution is investigated for the Burgers-Fisher equation in a very general form. The method is based on employing the monotonicity of the ratio of the Abelian integrals. However, the complexity of the nonlinear term increases the difficulty to prove its monotonicity. The obtained results generalize and improve the previous one (Zhang et al. Appl Math Lett 121:107353, 2021), and the new results in this paper have never appeared in the previous works including (Zhang et al. 2021).