Abstract
We consider the stability problem for the localized solutions of classical nonlinear spinor fields in space dimensions N=1 and N=3 within the framework of the Shatah-Strauss formalism. We show that the well-known relations existing between the different stability criteria for scalar field equations are no longer valid for spinor fields. We discuss the application of the Shatah-Strauss formalism to several models: e.g., the Gross-Neveu, Thirring, and the Soler models.
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