BEGIN:VCALENDAR VERSION:2.0 PRODID:Data::ICal 0.22 BEGIN:VEVENT DESCRIPTION:Professor Maxim Olchanyi (Olshanii)\, University of Massachuset ts Boston\n\n
The recently p roposed map [arXiv:2011.01415] between the hydrodynamic equations governin g the two-dimensional triangular cold-bosonic breathers [Phys. Rev. X 9\, 021035 (2019)] and the high-density zero-temperature triangular free-fermi onic clouds\, both trapped harmonically\, perfectly explains the former ph enomenon but leaves uninterpreted the nature of the initial (t=0) singular ity. This singularity is a density discontinuity that leads\, in the boson ic case\, to an infinite force at the cloud edge. The map itself becomes i nvalid at time 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\, alon g a ray in the direction normal to one of the three edges of the initial c loud\, 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 equ ation. More specifically\, under the Damski map\, the t=0 singularity of t he original problem becomes\, verbatim\, the initial condition for the wav e catastrophe solution found by Chandrasekhar in \;1943 [Ballistic Res earch Laboratory Report No. 423 (1943)]. At t=T/8\, our interpretation cea ses to exist: at this instance\, all three effectively one-dimensional sho ck waves emanating from each of the three sides of the initial triangle co llide at the origin\, and the 2D-1D correspondence between the solution of [arXiv:2011.01415] and the Damski-Chandrasekhar shock wave becomes invali d.
\n DTSTART:20211028T193000Z LOCATION:Online\, Room via Zoom SUMMARY:Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shoc k waves END:VEVENT END:VCALENDAR