  We describe the results of the two methods we developed to calculate the
stationary nonlinear solutions in one-dimensional plasmonic slot waveguides
made of a finite-thickness nonlinear dielectric core surrounded by metal
regions. These two methods are described in detail in the preceding article
[Walasik et al., submitted]. For symmetric waveguides, we provide the nonlinear
dispersion curves obtained using the two methods and compare them. We describe
the well known low-order modes and the higher-modes that were not described
before. All the modes are classified into two families: modes with and without
nodes. We also compare nonlinear modes with nodes with the linear modes in
similar linear slot waveguides with a homogeneous core. We recover the symmetry
breaking Hopf bifurcation of the first symmetric nonlinear mode toward an
asymmetric mode and we show that one of the higher modes also exhibits a
bifurcation. We study the behavior of the bifurcation of the fundamental mode
as a function of the permittivities of a metal and a nonlinear core. We
demonstrate that the bifurcation can be obtained at low power levels in
structures with optimized parameters. Moreover, we provide the dispersion
curves for asymmetric nonlinear slot waveguides. Finally, we give results
concerning the stability of the fundamental symmetric mode and the asymmetric
mode that bifurcates from it using both theoretical argument and numerical
propagation simulations from two different full-vector methods. We investigate
also the stability properties of the first antisymmetric mode using our two
numerical propagation methods.
