The compact and noncompact structures for two types of generalized Camassa–Holm–KP equations

The objective of this paper is to investigate two types of generalized nonlinear Camassa–Holm–KP equations in ( 2 + 1 ) dimensional space. Compactons, solitons, solitary patterns, periodic solutions and algebraic travelling wave solutions are expressed analytically under various circumstances. The conditions that cause the qualitative change in the physical structures of the solutions are emphasized.