Dynamic Behavior of Traveling Wave Solutions for a class for the time-space coupled fractional kdV system with time-dependent coefficients

In this paper, a simpli?ed bilinear method combined with a fractional trans- form has been used to obtain a new multiple soliton solutions for the Fractional coupled fractional kdV equations with variable coe?cients. These systems appear in biology, engineering, mechanics, complex physics phenomena economics, signal image proces- sing, notably control theory, groundwater problems and chemistry. Dispersion relations on the e?ects of the inhomogeneities of the model "due to the variable coe?cients" are derived and interpreted for deterministic of the characteristic-line and velocity of each obtained soliton waves.