General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces

In this paper we present a general and unified approach for analyzing the genuinely nonlinear dispersive mK(n,n) equations. The focusing branch exhibits compactons: solitons with finite wave lengths, whereas the defocusing branch supports solutions with solitary patterns. The work formally shows how to construct compact and noncompact solutions for mK(n,n) equations in one-, two- and three-dimensional spatial domains. Two distinct general formulae for each model, that are of substantial interest, are developed for all positive integers n, n>1