  We analyze nonlinear properties of microstructured materials with negative
refraction, the so-called left-handed metamaterials. We demonstrate that the
hysteresis-type dependence of the magnetic permeability on the field intensity
allows changing the material properties from left- to right-handed and back.
Using the finite-difference time-domain simulations, we study wave transmission
through the slab of nonlinear left-handed material, and predict existence of
temporal solitons in such materials. We demonstrate also that nonlinear
left-handed metamaterials can support both TE- and TM-polarized self-trapped
localized beams, spatial electromagnetic solitons. Such solitons appear as
single- and multi-hump beams, being either symmetric or antisymmetric, and they
can exist due to the hysteresis-type magnetic nonlinearity and the effective
domains of negative magnetic permeability.
