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Description
A deformed Toda model coupled to Dirac field (DATM) is considered. The DATM is regarded as a quasi-integrable model since it is a deformation of the integrable affine Toda model coupled to matter by introducing a scalar potential. It is defined as a fermion and scalar fields chirally coupled plus a scalar self-coupling potential. We show that it has remarkable properties with spectra compossed by Majorana zero-modes, in-gap and in the continuum bound states. In order to find the soliton-fermion solutions we make use of the tau function formalism. Our results may find many applications in several branches of non-linear physics, such as QCD$_2$, superfluidity, superconductivity and quantum computing.