  We consider the nonlinear Dirac equations in one dimension and review various
results on global existence of solutions in H1. Depending on the character of
the nonlinear terms, existence of the large-norm solutions can be extended for
all times. Global existence of the small-norm solutions is proved for the most
general nonlinear Dirac equations with cubic and higher-order nonlinear terms.
Integrability of the massive Thirring model is used to find conditions that no
solitons occur in the Cauchy problem with small initial data in a subspace of
L2.
