Compactons and solitary patterns structures for variants of the KdV and the KP equations

摘要

In this paper we discuss mathematical variants in higher dimensions of the KdV and the 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 study presents a fairly complete understanding of the compact and noncompact dispersive structures.