We present a general framework for constructing singular solutions of nonlinear evolution
equations that become singular on a d-dimensional sphere, where d> 1. The asymptotic
profile and blowup rate of these solutions are the same as those of solutions of the
corresponding one-dimensional equation that become singular at a point. We provide a
detailed numerical investigation of these new singular solutions for the following equations:
The nonlinear Schrödinger equation iψt (t, x)+ Δψ+| ψ| 2σψ= 0 with σ> 2, the biharmonic …