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 Schrodinger 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.

Automated summary

The study of nonlinear waves that collapse in finite time is of universal interest in various disciplines. In this study, a normal form for the emergence of radially symmetric blowup solutions from stationary ones in the nonlinear Schrodinger equation is systematically derived. This normal form, based on asymptotics beyond all algebraic orders, shows good agreement with numerics in both leading and higher-order effects, and is applicable to both infinite and finite domains in critical and supercritical regimes.