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We consider the Principal Chiral Field model posed in 1+1 dimensions into the Lie group SL(2, R). In this work we show the nonlinear stability of small enough nonsingular solitons. The method of proof involves the use of vector field methods as in a previous work by the second and third authors dealing with the Einstein's field equations under the Belinski-Zakharov formalism, extending for all times the size of suitable null weighted norms of the perturbations at time zero.
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Alejo et al. (2024) studied this question.
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