Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation

The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g.
within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential
example of the nonlinear Schr¨odinger equation and systematically derive a normal form for the
emergence of radially symmetric blowup solutions from stationary ones. While this is an extensively
studied problem, such a normal form, based on the methodology of asymptotics beyond all algebraic
orders, applies to both the dimension-dependent and power-law-dependent bifurcations previously
studied; it yields excellent agreement with numerics in both leading and higher-order effects; it
is applicable to both infinite and finite domains; and it is valid in both critical and supercritical
regimes.