In , the author constructs the theory of reticular Legendrian unfoldings that describes stable and generic multi-bifurcations of wavefronts generated by a hypersurface germ with a boundary, a corner, or an -corner.
In the case , the hypersurface has no boundary; a two-parameter family of wavefronts is given by a generating family defined on such that
In the case , the hypersurface has a boundary; a reticular Legendrian unfolding gives the wavefront , where the set is the wavefront generated by the hypersurface at time , and the set is the wavefront generated by the boundary of the hypersurface at time .
A reticular Legendrian unfolding has a generating family. Then the wavefront is given by the generating family defined on such that
Typical multi-bifurcations of wavefronts in 2D and 3D are defined by generic reticular Legendrian unfoldings for the cases . Their generating families are stably reticular -- equivalent to one of the following:
In the case , :
, , , , ,
In the case :
, , , .
 V. I. Arnold, Singularities of Caustics and Wave Fronts, Dordrecht: Kluwer Academic Publishers, 1990.
 V. I. Arnold, S. M. Gusein–Zade, and A. N. Varchenko, Singularities of Differential Maps, Volume I: The Classification of Critical Points, Caustics and Wave Fronts (Monographs in Mathematics, Vol. 82), Basel: Birkhäuser, 1985.