General compactons solutions for the focusing branch of the nonlinear dispersive K(n,n) equations in higher-dimensional spaces

摘要

In this paper, we will study the focusing branch of the genuinely nonlinear dispersive K(n,n) equation that exhibits compactons: solitons with finite wavelengths. The equation will be studied in one-, two- and three-dimensional spaces. General formulas for compactons solutions are developed for all positive integers n, n>1. Two sets of entirely new formulas, one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n, n>1, are established.