Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions.The main aim is to use a new method known as the (G’/G) method to exhibit the effects of dust charge fluctuations on the evolution of nonlinear waves.The coherent features of the shock and solitary waves along with the generation of high-energy waves have been amplified through the solution of the Korteweg-de Vries-Burgers equation,and the different natures of the waves were found successfully.Results are discussed graphically with the thoughtful choice of typical plasma parameters from different space plasma environments,exactly those found in cosmic dusty plasmas laden in ionospheric auroral region,radial spokes of Saturn’s rings,planetary nebulae and solar F-corona region.All conclusions are in good accordance with the actual occurrences and could be of interest to further investigations of space.Moreover,the applicability of the present method is hoped to be a great enhancement by its use as ingenious mechanism used to evaluate the soliton dynamics and Burgers shock waves.