In this paper, we have investigated propagation of two beams coupled solely due to cross action effect, and the self action effect is completely absent (thirring type coupled propagation). We have identified existence surface for thirring type solitons in the parameter space of power and width ratio of the two beams. Every point on the surface gives the appropriate beams' parameters (powers and beams' widths) of the two beams to obtain a soliton pair. For the first time we have identified loci for the formation of stable breather pairs. It is identified that for each point of the solitonic surface there exists one hyperbolic locus such that every point on this locus gives parameters for a stable breather pair.

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