EXACT SOLUTIONS OF THE GENERALIZED POCHHAMMER-CHREE EQUATION WITH SIXTH-ORDER DISPERSION

Nonlinear waves described by the generalized Pochhammer-Chree equation are analytically investigated. The addition of the sixth-order dispersion term, which will drastically change the characteristics of the equation, is examined. We employ the sine-cosine method to derive a variety of exact solutions of distinct physical structures including solitons, compactons, periodic and solitary pattern solutions for the adopted model, in the presence of the sixth-order dispersion term. The solitary wave ansatz method is used as well to obtain bright, singular, and dark soliton solutions. Parametric conditions for the existence of the exact solutions are given. The obtained results show that the generalized Pochhammer-Chree equation with sixth order dispersion reveals the richness of explicit soliton and periodic solutions. It should be noted that the study of a new model admitting soliton-type solutions is very important and these solutions will be useful for future research work.