THE EXACT TRAVELING WAVE SOLUTIONS OF LOCAL FRACTIONAL GENERALIZED HIROTA–SATSUMA COUPLED KORTEWEG–DE VRIES EQUATIONS ARISING IN INTERACTION OF LONG WAVES

Zong-Guo Zhang, Su-Ling Chen and Quan-Sheng Liu
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Zong-Guo Zhang: Division of Mathematics and Artificial Intelligence, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China
Su-Ling Chen: College of Intelligence and Information Engineering, Shandong University of Traditional Chinese Medicine, Jinan 250355, P. R. China
Quan-Sheng Liu: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-9

Abstract: Wave–wave interaction occurs in the propagation deformation of nonlinear long waves in shallow-water. In order to further study the propagation mechanism of shallow-water long waves interaction, the exact traveling wave solutions of the local fractional generalized Hirota–Satsuma coupled Korteweg–de Vries (HS-KdV) equations defined by the Cantor sets are obtained. The non-differentiable solutions with fixed fractal dimension and different propagation velocity are discussed. The results indicate that the exact solutions of the local fractional generalized HS-KdV equations characterize the interaction of fractal long waves with different dispersion relations on shallow-water surfaces.

Keywords: Exact Traveling Wave Solution; Local Fractional Hirota–Satsuma Coupled Korteweg–de Vries Equations; Long Wave Interaction; Fractals (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401205

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