  We study both linear and nonlinear surface waves localized at the interface
separating a left-handed medium (i.e. the medium with both negative dielectric
permittivity and negative magnetic permeability) and a conventional (or
right-handed) dielectric medium. We demonstrate that the interface can support
both TE- and TM-polarized surface waves - surface polaritons, and we study
their properties. We describe the intensity-dependent properties of nonlinear
surface waves in three different cases, i.e. when both the LH and RH media are
nonlinear and when either of the media is nonlinear. In the case when both
media are nonlinear, we find two types of nonlinear surface waves, one with the
maximum amplitude at the interface, and the other one with two humps. In the
case when one medium is nonlinear, only one type of surface wave exists, which
has the maximum electric field at the interface, unlike waves in right-handed
materials where the surface-wave maximum is usually shifted into a
self-focussing nonlinear medium. We discus the possibility of tuning the wave
group velocity in both the linear and nonlinear cases, and show that
group-velocity dispersion, which leads to pulse broadening, can be balanced by
the nonlinearity of the media, so resulting in soliton propagation.
