© 2015, Springer Science+Business Media Dordrecht.This paper addresses Boussinesq equation with power law nonlinearity and dual dispersion that is the study of water waves in Fluid Dynamics. Three integration algorithms retrieve solitons and other solutions to model. The three integration algorithms applied are trial solution method, (Formula presented.) -expansion approach as well as extended trial equation method. The solitons are solitary waves, shock waves as well as singular. As a by-product, several other solutions are listed from these integration schemes. These are singular periodic solutions and plane waves. All of these solutions have respective constraint relations that are needed for the solution to hold.