solving the nonlinear circular equation by the homotopy analysis method for te polarized wave

In this work, we study te-polarized electromagnetic waves propagating in aninhomogeneous dielectric waveguide of circular cross section filled with a nonlinearmedium; most perturbation methods assume a small parameter exists, but mostnonlinear problems have no small parameter at all. homotopy analysis method(ham) was proposed to obtain series solutions for nonlinear differential equations.the main benefit of the ham method is that it does not depend on a smallparameters.