Resumo:
This dissertation investigates aspects of integrability in (1+1)-dimensional field theories,
with emphasis on the coupled Thirring model. Initially, the foundations of classical integrability
are presented, including Liouville integrability, the zero-curvature formalism, and
Bäcklund transformations. Subsequently, the sine-Gordon model and the massive Thirring
model are analyzed from the perspective of their integrable structures. The main focus of
this work lies on the coupled Grassmannian Thirring model, in which the Lax connection
based on the superalgebra 𝑠𝑙(2, 1) is explicitly constructed, ensuring the classical integrability
of the system. The Bäcklund transformations are generalized and the permutability
property is analyzed, allowing for the systematic construction of multiparametric solutions.
It is noteworthy that the explicit attainment of these multiparametric solutions for
the coupled model constitutes a novel result in the literature. It is expected that such
solutions are related to N-soliton solutions of the bosonic version of the coupled model.
