DYNAMIC BEHAVIOR OF TRAVELING WAVE SOLUTIONS FOR A CLASS FOR THE TIME-SPACE COUPLED FRACTIONAL kdV SYSTEM WITH TIME-DEPENDENT COEFFICIENTS

Abstract

In this paper, a simplified bilinear method combined with a fractional transform has been used to obtain a new multiple soliton solutions for the Fractional coupled fractional kdV equations with variable coefficients.  These systems appear in biology, engineering, mechanics, complex physics phenomena economics, signal image processing, notably control theory, groundwater problems and chemistry.  Dispersion relations on the effects 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.