The recently proposed map [arXiv:2011.01415] between the hydrodynamic
equations governing the two-dimensional triangular cold-bosonic breathers
[Phys. Rev. X 9, 021035 (2019)] and the high-density zero-temperature
triangular free-fermionic clouds, both trapped harmonically, perfectly explains
the former phenomenon but leaves uninterpreted the nature of the initial
(t=0) singularity. This singularity is a density discontinuity that leads, in
the bosonic case, to an infinite force at the cloud edge. The map itself
becomes invalid at times t<0. A similar singularity appears at t=T/4,
where T is the period of the harmonic trap, with the Fermi-Bose map becoming
invalid at t>T/4. Here, we first map -- using the scale invariance of the
problem -- the trapped motion to an untrapped one. Then we show that in the new
representation, the solution [arXiv:2011.01415] becomes, along a ray in the
direction normal to one of the three edges of the initial cloud, a freely
propagating one-dimensional shock wave of a class proposed by Damski in [Phys.
Rev. A 69, 043610 (2004)]. There, for a broad class of initial conditions, the
one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers'
equation, a nonlinear transport equation. More specifically, under the Damski
map, the t=0 singularity of the original problem becomes, verbatim, the
initial condition for the wave catastrophe solution found by Chandrasekhar in
1943 [Ballistic Research Laboratory Report No. 423 (1943)]. At t=T/8, our
interpretation ceases to exist: at this instance, all three effectively
one-dimensional shock waves emanating from each of the three sides of the
initial triangle collide at the origin, and the 2D-1D correspondence between
the solution of [arXiv:2011.01415] and the Damski-Chandrasekhar shock wave
becomes invalid.Comment: 13 pages, 2 figures. Submission to SciPos
