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arXiv · 2008.08968

A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation

S. J. Chapman·M. E. Kavousanakis·I. G. Kevrekidis·P. G. Kevrekidis
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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.

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S. J. Chapman, M. E. Kavousanakis, I. G. Kevrekidis, P. G. Kevrekidis. 2020-08-20. A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation. https://doi.org/10.1103/physreve.104.044202

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