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Traveling Wave Solution of Bad and Good Modified Boussinesq Equations with Conformable Fractional-Order Derivative

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Abstract

In this paper we investigate the fractional order derivative Bad and Good modified equations via the bifurcation theory of dynamical systems method. To convert the fractional order derivative equations into ODEs, we utilize the transformation \( u(x,t)=\phi (\xi ),\,\,\, \xi =x-c t^\alpha \), instead of the commonly use \(\xi =x-c\frac{t^\alpha }{\alpha } \). Bright and dark solitons, kink and anti-kink solutions, as well as periodic wave solutions are obtained. We show that the wavelength and amplitude of the traveling wave solutions depend on the fractional-order \(\alpha \).

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Funding

Funding was provided by National Natural Science Foundation of China (Grand No. 11671176).

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  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    N’Gbo N’Gbo & Yonghui Xia

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  1. N’Gbo N’Gbo
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Correspondence to Yonghui Xia.

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N’Gbo, N., Xia, Y. Traveling Wave Solution of Bad and Good Modified Boussinesq Equations with Conformable Fractional-Order Derivative. Qual. Theory Dyn. Syst. 21, 14 (2022). https://doi.org/10.1007/s12346-021-00541-2

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