New solitary wave solutions with compact support and Jacobi elliptic function solutions for the nonlinearly dispersive Boussinesq equations

In this paper, we establish exact special solutions for the nonlinearly dispersive Boussinesq equations. A new extended sn–cn method is used for obtaining compacton, solitary patterns, solitary wave, periodic wave and Jacobi elliptic function solutions for this equation with minimal calculations. As a result, abundant new compactons:solitons with the absence of infinite wings, solitary pattern solutions having infinite slopes or cups, solitary wave, periodic wave solutions and Jacobi elliptic function solutions are obtained.