Compactons dispersive structures for variants of the K(n,n) and the KP equations

In this paper we discuss two generalized forms of the K(n,n) and the KP equations that exhibit compactons: solitons with the absence of infinite wings, and solitary patterns solutions having infinite slopes or cusps. The variants are extended to include nonlinear dispersion to support compactons structures and solitary patterns in higher dimensions. Two distinct general formulas for compact and noncompact solutions, that are of substantial interest, are formally developed.