N-fold Darboux transformation and explicit solutions in terms of the determinant for the three-field Blaszak–Marciniak lattice

In this work, the three-field Blaszak–Marciniak (BM) lattice is investigated via the N -fold Darboux transformation (DT) technique. As a result, the N -fold DT for a spectral problem associated with the three-field BM lattice is constructed, and the explicit solutions in terms of the determinant are presented via the N -fold DT. Some inelastic interaction evolution phenomena arising for the three-soliton solutions are studied graphically. Results in this work may be helpful for interpreting certain physical phenomena.