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Near-Ordinary Periodic Waves of a Generalized Reaction–Convection–Diffusion Equation

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Abstract

We investigate near-ordinary periodic traveling wave solutions bifurcated from a family of ordinary periodic traveling wave solutions for a generalized reaction–convection–diffusion equation, especially its dependence on the nonlinear reaction. Using the Abelian integral method and the Chebyshev criteria, we find conditions for the existence and number of near-ordinary periodic wave solutions not only for the monotone case of the ratio of the Abelian integral as previous publications, but also for the non-monotone case. In a parameter region we provide a conjecture about the uniqueness of near-ordinary periodic traveling wave solutions for any degree of the nonlinear reaction and prove it up to degree four. The final simulations illustrate theoretical results numerically.

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Acknowledgements

The second author thanks the support of the National Natural Science Foundation of China (No. 12271378).

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Minzhi Wei & Xingwu Chen

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  1. Minzhi Wei
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  2. Xingwu Chen
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Minzhi Wei wrote the main manuscript text after discussing main technique and computations with Xingwu Chen. All authors reviewed the manuscript.

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Correspondence to Xingwu Chen.

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Wei, M., Chen, X. Near-Ordinary Periodic Waves of a Generalized Reaction–Convection–Diffusion Equation. Qual. Theory Dyn. Syst. 22, 107 (2023). https://doi.org/10.1007/s12346-023-00807-x

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