The present article deals with semi-linear hyperbolic boundary value problems defined in the strip geometry. After having established a strong well-posedness result by using a rather classical linear scheme of approximation, we address the question of the construction of approximate solutions by geometric optics expansions methods. On the one hand because the problem is semi-linear, the non linearity creates one self-interaction of the phases: the generation of harmonics. Such a self-interaction is classical. But, on the other hand, because of the geometry of the strip, a phase can regenerate itself by repeated reflections against the two sides of the boundary. Consequently we have an other self-interaction phenomenon. A natural question is to ask if these two phenomena can interact the one with the other. We here show and rigorously justify that the answer of the above question. The reason being essentially that one phenomenon occurs in the interior while the second one is located at the boundary.