Two-point gradient-catastrophe conjecture for focusing semiclassical DS II

Consider generic rapidly decreasing initial data with a single hump for the focusing semiclassical DS II system, and let $x_c$ and $y_c$ denote the spatial coordinates of gradient-catastrophe points. Focusing DS II gradient-catastrophe conjecture. Solutions develop two points of gradient catastrophe in finite time. At each point only one component of the gradient is unbounded; the singularity is one-dimensional, with local behavior $(x-x_c)^{1/2}$ or $(y-y_c)^{1/2}$ in the corresponding spatial direction. If the initial data are invariant under interchange of $x$ and $y$, the two points coincide. This is a numerical conjecture about the generic singularity structure of focusing semiclassical DS II; the source does not provide a proof.