Comment on: “Solving the conformable Huxley equation using the complex method” [Electron. Res. Arch., 31 (2023), 1303–1322]

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Abstract

Using the complex method, Guoqiang Dang and Qiyou Liu [Guoqiang Dang, Qiyou Liu, Electron. Res. Arch., 31 (2023), 1303–1322] have found some exact solutions of the conformable Huxley equation. In this comment, we first demonstrate that the elliptic function solutions and rational function solutions do not satisfy the complex conformable Huxley equation. Finally, all exact solutions of the conformable Huxley equation are given by us.

Keywords

differential equation / exact solution / meromorphic function / complex method / conformable Huxley equation

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References

[1] G. Dang, Q. Liu, Solving the conformable Huxley equation using the complex method, Electron. Res. Arch., 31 (2023), 1303-1322. https://doi.org/10.3934/era.2023067

[2] W. J. Yuan, Y. D. Shang, Y. Huang, H. Wang, The representation of meromorphic solutions of certain ordinary differential equations and its applications, Sci. Sin. Math., 43 (2013), 563-575. https://doi.org/10.1360/012012-159

[3] W. J. Yuan, Y. Z. Li, J. M. Lin, Meromorphic solutions of an auxiliary ordinary differential equation using complex method, Math. Meth. Appl. Sci., 36 (2013), 1776-1782. https://doi.org/10.1002/mma.2723

[4] W. J. Yuan, Y. Huang, Y. D. Shang, All travelling wave exact solutions of two nonlinear physical models, Appl. Math. Comput., 219 (2013), 6212-6223. https://doi.10.1016/j.amc.2012.12.023

[5] W. J. Yuan, Z. Huang, M. Fu, J. Lai, The general solutions of an auxiliary ordinary differential equation using complex method and its applications, Adv. Differ. Equations, 2014 (2014), 1-9. https://doi.org/10.1186/1687-1847-2014-147

[6] W. J. Yuan, B. Xiao, Y. Wu, J. Qi, The general traveling wave solutions of the Fisher type equations and some related problems, J. Inequal. Appl., 2014 (2014), 1-15. https://doi.org/10.1186/1029-242X-2014-500

[7] W. J. Yuan, Y. H. Wu, Q. H. Chen, Y. Huang, All meromorphic solutions for two forms of odd order algebraic differential equations and its applications, Appl. Math. Comput., 240 (2014), 240-251. https://doi.org/10.1016/j.amc.2014.04.099

[8] W. J. Yuan, W. L. Xiong, J. M. Lin, Y. H. Wu, All meromorphic solutions of an auxiliary ordinary differential equation using complex method, Acta. Math. Sci., 35 (2015), 1241-1250. https://doi.org/10.1016/S0252-9602(15)30052-7

[9] A. C. Cevikel, A. Bekir, E. H. M. Zahran, Novel exact and solitary solutions of conformable Huxley equation with three effective methods, J. Ocean Eng. Sci., 2022 (2022). https://doi.org/10.1016/j.joes.2022.06.010

[10] R. Conte, T. W. Ng, C. F. Wu, Hayman’s classical conjecture on some nonlinear second-order algebraic ODEs, Complex Var. Elliptic Equations, 60 (2015), 1539-1552. https://doi.org/10.1080/17476933.2015.1033414

[11] W. J. Yuan, F. N. Meng, J. M. Lin, Y. H. Wu, All meromorphic solutions of an ordinary differential equation and its applications, Math. Meth. Appl. Sci., 39 (2016), 2083-2092. https://doi.10.1002/mma.3625