Peakons, kinks, compactons and solitary patterns solutions for a family of Camassa–Holm equations by using new hyperbolic schemes

In this paper, a family of Camassa–Holm equations with distinct parameters is investigated. New solitary wave solutions that include peakons, kinks, compactons, solitary patterns solutions, and plane periodic solutions are formally derived. New schemes that rest mainly on hyperbolic functions are employed to achieve our goal. The work highlights the qualitative change in the physical structures of the obtained solutions.