The sub-ODE method for finding exact travelling wave solutions of generalized nonlinear Camassa–Holm, and generalized nonlinear Schrödinger equations

With the aid of the ordinary differential equation (ODE) involving an arbitrary positive power of dependent variable proposed by Li and Wang and an indirect F-function method very close to the F-expansion method, we solve the generalized Camassa–Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p)C(l,n,p) and the generalized nonlinear Schrödinger equation with nonlinear dispersion GNLS(l,n,p,q)GNLS(l,n,p,q). Taking advantage of the new subsidiary ODE, this F-function method is used to map the solutions of C(l,n,p)C(l,n,p) and GNLS(l,n,p,q)GNLS(l,n,p,q) equations to those of that nonlinear ODE. As result, we can successfully obtain in a unified way, many exact solutions.