  We present two complementary models to study stationary nonlinear solutions
in one-dimensional plasmonic slot waveguides made of a finite-thickness
nonlinear dielectric core surrounded by metal regions. The considered
nonlinearity is of focusing Kerr type. In the first model, it is assumed that
the nonlinear term depends only on the transverse component of the electric
field and that the nonlinear refractive index change is small compared to the
linear part of the refractive index. This first model allows us to describe
analytically the field profiles in the whole waveguide using Jacobi elliptic
special functions. It also provides a closed analytical formula for the
nonlinear dispersion relation. In the second model, the full dependency of the
Kerr nonlinearity on the electric field components is taken into account and no
assumption is required on the amplitude of the nonlinear term. The disadvantage
of this approach is that the field profiles must be computed numerically.
Nevertheless analytical constraints are obtained to reduce the parameter space
where the solutions of the nonlinear dispersion relations are sought.
