A class of nonlinear fourth order variant of a generalized Camassa–Holm equation with compact and noncompact solutions

摘要

In this paper we study a class of nonlinear fourth order analogue of a generalized Camassa–Holm equation. It is shown that this class gives compactons, conventional solitons, solitary patterns and periodic solutions. It is also found that the qualitative change in the physical structure of solutions depends mainly on the exponent of the wave function u(x, t), positive or negative, and on the coefficient of (un)ξξ as well.