General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces

摘要

In this work, the defocusing branch of the genuinely nonlinear dispersive K(n,n) equation that exhibits solutions with solitary patterns is investigated. The equation, with constant coefficients to the derivatives, is examined in one-, two- and three-dimensional spaces. General formulas for solutions with solitary patterns are developed for all positive integers n,n>1. Two sets of entirely new formulas, one set produces solutions for even integers n whereas the second set produces solutions in opposite directions for odd integers n,n>1, are established.