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- Title
THE EXACT TRAVELING WAVE SOLUTIONS OF LOCAL FRACTIONAL GENERALIZED HIROTA–SATSUMA COUPLED KORTEWEG–DE VRIES EQUATIONS ARISING IN INTERACTION OF LONG WAVES.
- Authors
ZHANG, ZONG-GUO; CHEN, SU-LING; LIU, QUAN-SHENG
- 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.
- Subjects
KORTEWEG-de Vries equation; CANTOR sets; NONLINEAR evolution equations; NONLINEAR waves; DISPERSION relations; FRACTAL dimensions
- Publication
Fractals, 2024, Vol 32, Issue 4, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X23401205