The effect of the order of nonlinear dispersive equation on the compact and noncompact solutions

摘要

The effect of the order of nonlinear dispersive partial differential equation on the compact and noncompact solutions is studied in this paper. Two variants of the KdV equation of odd orders are examined. Our analysis reveals that the physical nature of these nonlinear KdV-type of equations are different. Two distinct sets of general formulas for each type of variants are performed to present a fairly complete understanding of the compact and noncompact structures.