Solitons, shock waves, conservation laws and bifurcation analysis of boussinesq equation with power law nonlinearity and dual dispersion

This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to extract the conservation laws of this equation. © 2014 NSP Natural Sciences Publishing Cor.