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A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation
- Source :
- Phys. Rev. E 104, 044202 (2021)
- Publication Year :
- 2020
-
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.
- Subjects :
- Nonlinear Sciences - Pattern Formation and Solitons
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. E 104, 044202 (2021)
- Publication Type :
- Report
- Accession number :
- edsarx.2008.08968
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevE.104.044202