  In this paper we numerically analyze the 1D self-localized solutions of the
Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral
renormalization method (SRM) and compare our findings with those solutions of
the nonlinear Schrodinger equation (NLSE). We show that single, dual and
N-soliton solutions exist for the case with zero optical potentials, i.e. V=0.
We also show that these soliton solutions do not exist, at least for a range of
parameters, for the photorefractive lattices with optical potentials in the
form of V=Io cos^2(x) for cubic nonlinearity. However, self-stable solutions of
the KEE with saturable nonlinearity do exist for some range of parameters. We
compare our findings for the KEE with those of the NLSE and discuss our
results.
