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

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.