Journal article
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 Schr¨odinger 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, 1.4MB, Terms of use)
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- Publisher copy:
- 10.1103/PhysRevE.104.044202
Authors
- Publisher:
- American Physical Society
- Journal:
- Physical Review E: Statistical, Nonlinear, and Soft Matter Physics More from this journal
- Volume:
- 104
- Article number:
- 044202
- Publication date:
- 2021-10-04
- Acceptance date:
- 2021-09-13
- DOI:
- EISSN:
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1550-2376
- ISSN:
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1539-3755
- Language:
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English
- Keywords:
- Pubs id:
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1194192
- Local pid:
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pubs:1194192
- Deposit date:
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2021-09-20
Terms of use
- Copyright holder:
- American Physical Society
- Copyright date:
- 2021
- Rights statement:
- © 2021 American Physical Society
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from American Physical Society at: https://doi.org/10.1103/PhysRevE.104.044202
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