  The concept of transformation optics is extended to nonlinear
electrodynamics. It is shown that transformation optics favors implicit
constitutive relations in terms of energy densities D.E and B.H rather than E^2
and H^2. The Kerr nonlinearity is studied in detail and the transformation
optics based engineering of self-interaction effects is discussed. As a
specific example we introduce transformation optics applied on a self-focusing
field configuration.
