The Camassa-Holm-KP equations with compact and noncompact travelling wave solutions

In this paper, two variants of Camassa-Holm-KP equations are investigated. Compactons: solitons with the absence of infinite tails, solitons: nonlinear localized waves of infinite support, solitary patterns having infinite slopes or cusps, and plane periodic solutions are formally derived. The work highlights the qualitative change in the physical structures of the obtained solutions.