Shock waves and other solutions to the Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity

We study the hybrid Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. Three different techniques - the ansatz method, Lie-symmetry analysis and the (G′/G)-expansion method - are used to find shock wave solutions. Several constraint conditions naturally emerge that guarantee the existence of shock waves. We discuss the nature of the solutions generated by the different methods.