Geometrically constrained multifield models with BNRT solutions

In this paper, we investigate multifield models in which the two-field BNRT model is coupled to a third field through mediator functions in the Lagrangian density. To conduct the investigation, we obtain the equations of motion and develop a first-order formalism based on energy minimization. Two possibilities are considered: (i) the third field acting in the mediator functions to modify the BNRT solutions; (ii) the BNRT fields feeding the mediator function to produce effects in the kink solution of the third field. In the case (i), the results show that the solutions may be related to the standard ones with the coordinate redefined in terms of the mediator functions if they are equal. This allows to induce effects similar to geometric constrictions in the core, or to compactify the tail of the BNRT solutions. If the mediator functions differ one from another, we show that the effects are distinct, with the compactification of just one of the two-field solutions. In the case (ii), the orbit parameter of the model plays an important role, modifying the mediator function that induces changes in the profile of the kink associated to the third field.