Controllable dynamical behaviors and the analysis of fractal Burgers hierarchy with the full effects of in homogeneities of media

The aim of this work is three fold. First, via a fractional complex transformation and a simplified bilinear method, N-shock-wave solutions for the variable-coefficient fractal Burgers equations are obtained, with their relevant properties and features being illustrated. The explicit functions describing the evolution of the amplitude, phase, and velocity are also given. Second, through the characteristic-line method and graphical analysis we discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Finally, a new approach to control the effects of inhomogeneities of media and nonuniformities of boundaries on the soliton behavior is suggested.