Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation
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...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Physical Society
2021
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| _version_ | 1826302331658960896 |
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| author | Chapman, SJ Kavousanakis, M Kevrekidis, IG Kevrekidis, PG |
| author_facet | Chapman, SJ Kavousanakis, M Kevrekidis, IG Kevrekidis, PG |
| author_sort | Chapman, SJ |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T05:45:56Z |
| format | Journal article |
| id | oxford-uuid:e7374bcc-c5ef-4874-9c03-4707aafc3ac6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:45:56Z |
| publishDate | 2021 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:e7374bcc-c5ef-4874-9c03-4707aafc3ac62022-03-27T10:37:01ZNormal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e7374bcc-c5ef-4874-9c03-4707aafc3ac6EnglishSymplectic ElementsAmerican Physical Society2021Chapman, SJKavousanakis, MKevrekidis, IGKevrekidis, PGThe 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. |
| spellingShingle | Chapman, SJ Kavousanakis, M Kevrekidis, IG Kevrekidis, PG Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation |
| title | Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation |
| title_full | Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation |
| title_fullStr | Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation |
| title_full_unstemmed | Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation |
| title_short | Normal form for the onset of collapse: the prototypical example of the nonlinear Schrodinger equation |
| title_sort | normal form for the onset of collapse the prototypical example of the nonlinear schrodinger equation |
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