Bell shape solitary, anti-kink solitary and periodic wave solutions of the Benjamin Ono equation for shallow water waves

In this study, the Benjamin Ono equation which acts a key role for the shallow water waves is explored. Two effective approaches namely the Bernoulli sub-equation function method and simple frequency formulation method are adopted to extract some different wave solutions, which include the bell shape solitary, anti-kink solitary and periodic wave solutions. Correspondingly, the outlines of the diverse wave solutions are unveiled graphically through MAPLE.