In this paper, with the help of the Lucas Riccati method and a  linear variable separation method, variable separation solutions of  the -dimensional modified dispersive water-wave system are obtained. We give the positive answer for the following question:  Are there any localized excitations derived by the use of another functions? For this purpose, some attention will be paid to dromion, peakon, dromion lattice, multi dromion-solitoff excitations, regular fractal dromions, lumps with self-similar structures and stochastic fractal dromion structures based on the golden mean. By the novel definition of modified Weierstrass function, we discussed the stochastic fractal dromion structure.

Lucas functions, localized excitations, variable separation solutions, -dimensional modified dispersive water-wave system.