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