Compact and noncompact structures for a variant of KdV equation in higher dimensions

摘要

In this paper we study two mathematical variants of KdV equation. We show that the focusing branches of these variants exhibit compactons: solitons with finite wavelength, whereas the defocusing branches support solitary patterns solutions with cusps or infinite slopes. A framework is developed for studying these problems in higher dimensions. Two distinct sets of general formulas for each type of variants are developed to present a fairly complete understanding of the compact and noncompact dispersive structures.