New compact and noncompact structures of the nonlinearly dispersive Boussinesq equations

In this paper, we establish exact solutions for the nonlinear Boussinesq equations by using the sn-cn method. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary pattern solutions having infinite slopes or cups, solitary wave and periodic wave solutions of this equations are obtained. The properties of the B(m,n) equations are shown in figures.