Limit cycles of piecewise smooth differential systems of the type nonlinear centre and saddle

Piecewise linear differential systems separated by two parallel straight lines of the type of centre-centre-Hamiltonian saddle and the centre-Hamiltonian saddle-Hamiltonian saddle can have at most one limit cycle and there are systems in these classes having one limit cycle. In this paper, we study the limit cycles of a piecewise smooth differential system separated by two parallel straight lines formed by nonlinear centres and a Hamiltonian saddle.