  Two distinct models are developed to investigate the transverse magnetic
stationary solutions propagating in one-dimensional anisotropic nonlinear
plasmonic structures made from a nonlinear metamaterial core of Kerr-type
embedded between two semi-infinite metal claddings. The first model is
semi-analytical, in which we assumed that the anisotropic nonlinearity depends
only on the transverse component of the electric field and that the nonlinear
refractive index modification is small compared to the linear one. This method
allows us to derive analytically the field profiles and the nonlinear
dispersion relations in terms of the Jacobi elliptical functions. The second
model is fully numerical, it is based on the finite-element method in which all
the components of the electric field are considered in the Kerr-type
nonlinearity with no presumptions on the nonlinear refractive index change. Our
finite-element based model is valid beyond weak nonlinearity regime and
generalize the well-known single-component fixed power algorithm that is
usually used. Examples of the main cases are investigated including ones with
strong spatial nonlinear effects at low powers. Loss issues are reduced through
the use of gain medium in the nonlinear metamaterial core.
