Compact structures for variants of the generalized KdV and the generalized KP equations

摘要

In this paper we discuss mathematical variants in higher dimensions of the generalized KdV and the generalized KP equations. It is shown that the focusing branches of these variants exhibit compactons: solitons with finite wavelength, whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps. The compact and the noncompact dispersive structures are examined in a general way.