Solitonic structures in a generalized dispersive Camassa-Holm model

Abstract

A generalized Camassa-Holm model is introduced to describe the irrotational incompressible flow for a shallow layer of inviscid fluid moving under the influence of gravity without surface tension when the model has a strong nonlinear dispersion. This physical model also contains a set of nonlinear terms. Rich regular and singular solitons are found when a transaction between nonlinearity and dispersion analysis is performed. Realizations of this model can be made in terms of restrictions on its exponential sequence. Besides compactons, kinks, periodic compactons and multiple compactons that are found, pair compactons which entitled for a simulation that has two coexisting symmetrical humps are taken into account. In a special case when the coefficient of term involving first-order derivative on x satisfies k=0, there occurs blow-up phenomena, as well as usual solitary pattern solutions. In addition, depending on the development of ansatz forms, with some combinations of the parameters, two families of symmetrical and non- symmetrical structures with peak-like wave crests are obtained in exact form.