Topological (dark) soliton solutions for the Camassa–Holm type equations

• The study of wave propagation on the surface of water has been a subject of consideration.
• Camassa–Holm type equations described the propagation of long waves in shallow water.
• Exact solutions of NWEs plays an important role in nonlinear physical phenomena.
• The existence of soliton solutions for nonlinear models is of great importance.

In this paper, the topological (dark) soliton solutions to the Camassa–Holm type equations are obtained by the solitary wave ansatz method. This solution may be useful to explain some physical phenomena in genuinely nonlinear dynamical systems that are described by Camassa–Holm type models.