  First, we point out that the present applied superposition principle is
linear, it must be developed into a generality. Next, the linear operators and
equations should be developed nonlinearly. They will include nonlinear
Klein-Gordon equation and Dirac equations, and corresponding Heisenberg
equation. The quantum commutation and anticommutation should be developed. This
theory may include the renormalization, which is the correction of Feynman
rules of curved closed loops. We think the interaction equations are nonlinear.
Many theories, models and phenomena are all nonlinear, for instance, soliton,
nonabelian gauge field, and the bag model, etc. The superluminal entangled
state, which relates the nonlocal quantum teleportation and nonlinearity,
should be a new fifth interaction. Moreover, the NL effects exist possibly for
four interactions, for single particle, for high energy, and for small
space-time, etc. The relations among NL theory and electroweak unified theory,
and QCD, and CP nonconservation, etc., are expounded. Finally, some known and
possible tests are discussed. The NL theory relates the possible decrease of
entropy in isolated system.
