Solitary patterns solutions having infinite slopes or cusps for fifth-order KdV like equations in higher dimensions

摘要

In this paper we consider a modified form of fifth-order KdV equation (fKdV) that exhibits solutions with solitary patterns having cusps or infinite slopes. We formally construct a framework for studying this problem in higher dimensions. Two distinct sets of general formulas, that are of substantial interest, are developed for this variant fK(n,n) for all positive integers n, n⩾1.