Periodic wave solutions for a generalized reaction-convection-diffusion equation of high-order (Q6592486)

This paper investigates the uniqueness of periodic wave solutions for a generalized reaction-convection-diffusion equation with arbitrarily high order reaction or convection term. The main technique is to prove the monotonicity of the ratio of two Abelian integrals by a new criterion and Descartes' rule of signs. In the main results, the authors give a positive answer to a conjecture made in [\textit{M. Wei} and \textit{X. Chen}, Qual. Theory Dyn. Syst. 22, No. 3, Paper No. 107, 21 p. (2023; Zbl 1518.35200)]. In addition, the authors prove the uniqueness of near-ordinary periodic wave solutions for any positive integer $n > 1$, arbitrarily high order convection term, and give some numerical results.