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One way of constructing explicit expressions of solutions of integrablesystems of Partial Differential Equations (PDEs) goes via the Darboux method.This requires the construction of Darboux matrices. Here we introduce a novelalgorithm to obtain such matrices in polynomial form. Our method is illustratedby applying it to the classical Massive Thirring Model (MTM), and by combiningit with the Dihedral group of symmetries possessed by this model.

Darboux polynomial matrices: the classical Massive Thirring Model as study case