Modified nonlinearly dispersive mK(m,n,k) equations: I. New compacton solutions and solitary pattern solutions Original Research Article

In this paper exact solutions of the modified nonlinearly dispersive KdV equations (simply called mK(m,n,k) equations), um−1ut+a(un)x+b(uk)xxx=0, are investigated by using some direct ansatze. As a result, abundant new compacton solutions: solitons with the absence of infinite wings, solitary pattern solutions having infinite slopes or cups, solitary wave solutions and periodic wave solutions are obtained.