1+1 SOLVABLE RELATIVISTIC FIELD MODELS

Nonlinear Lorentz invariant field models are constructed in such a way to be integrable by a transformation of a linear free field. The tran sformation is explicitly found by requiring that the U(1) conserved cu rrent keeps the same expression of the free field. This method is appl ied to the complex scalar and spinor fields in 1 + 1 dimensions. Local ized nondispersive waves exist and interact with each other. A way of introducing nonlinear interactions between different fields is also gi ven with the property of preserving integrability.