@article{200321,
  author = {S. J. Chapman and M. Kavousanakis and I. G. Kevrekidis and P. G. Kevrekidis},
  title = {Normal form for the onset of collapse: The prototypical example of the nonlinear Schr{\"o}dinger equation},
  abstract = { The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g., within optical, at., plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schr{\"o}dinger equation and systematically derive a normal form for the emergence of radially sym. blowup solutions from stationary ones. While this is an extensively studied problem, such a normal form, based on the methodol. 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. },
  year = {2021},
  journal = {Phys. Rev. E},
  volume = {104},
  number = {4},
  pages = {044202},
  publisher = {American Physical Society},
  isbn = {2470-00532470-0045},
  url = {https://doi.org/10.1103/PhysRevE.104.044202},
  language = {eng},
}