A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation
Abstract
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 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, unifies 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 all (subcritical, critical and supercritical) regimes.
Keywords
Cite
@article{arxiv.2008.08968,
title = {A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation},
author = {S. J. Chapman and M. E. Kavousanakis and I. G. Kevrekidis and P. G. Kevrekidis},
journal= {arXiv preprint arXiv:2008.08968},
year = {2021}
}