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Article: An exact, periodic solution of the Kaup-Newell equation
Title | An exact, periodic solution of the Kaup-Newell equation |
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Authors | |
Keywords | Derivative nonlinear Schrödinger (Kaup-Newell) equation Elliptic integrals of the third kind |
Issue Date | 2010 |
Publisher | Asian Academic Publisher Limited. The Journal's web site is located at http://www.nonlinearscience.com/journal_2076-2275.php |
Citation | Nonlinear Science Letters A: Mathematics, Physics and Mechanics, 2010, v. 1 n. 1, p. 83-89 How to Cite? |
Abstract | An exact, periodic solution of a special derivative nonlinear Schrödinger model, the Kaup–Newell equation incorporating cubic nonlinearity, is derived. The polar, or Madelung, representation is employed. The amplitude and the phase are expressed in terms of elliptic function and elliptic integral of the third kind respectively. Insisting on strict periodicity for both the amplitude and phase yields a ‘quantized’, or ‘eigenvalue’, condition for the modulus of the elliptic functions. Plane wave and solitary pulses are recovered in the appropriate limiting regimes. For intermediate values of the modulus, numerical results are presented. |
Persistent Identifier | http://hdl.handle.net/10722/207878 |
ISSN |
DC Field | Value | Language |
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dc.contributor.author | Chow, KW | - |
dc.date.accessioned | 2015-01-20T06:55:01Z | - |
dc.date.available | 2015-01-20T06:55:01Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Nonlinear Science Letters A: Mathematics, Physics and Mechanics, 2010, v. 1 n. 1, p. 83-89 | - |
dc.identifier.issn | 2076-2275 | - |
dc.identifier.uri | http://hdl.handle.net/10722/207878 | - |
dc.description.abstract | An exact, periodic solution of a special derivative nonlinear Schrödinger model, the Kaup–Newell equation incorporating cubic nonlinearity, is derived. The polar, or Madelung, representation is employed. The amplitude and the phase are expressed in terms of elliptic function and elliptic integral of the third kind respectively. Insisting on strict periodicity for both the amplitude and phase yields a ‘quantized’, or ‘eigenvalue’, condition for the modulus of the elliptic functions. Plane wave and solitary pulses are recovered in the appropriate limiting regimes. For intermediate values of the modulus, numerical results are presented. | - |
dc.language | eng | - |
dc.publisher | Asian Academic Publisher Limited. The Journal's web site is located at http://www.nonlinearscience.com/journal_2076-2275.php | - |
dc.relation.ispartof | Nonlinear Science Letters A: Mathematics, Physics and Mechanics | - |
dc.subject | Derivative nonlinear Schrödinger (Kaup-Newell) equation | - |
dc.subject | Elliptic integrals of the third kind | - |
dc.title | An exact, periodic solution of the Kaup-Newell equation | en_US |
dc.type | Article | en_US |
dc.identifier.email | Chow, KW: kwchow@hku.hk | - |
dc.identifier.hkuros | 170642 | - |
dc.identifier.volume | 1 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 83 | - |
dc.identifier.epage | 89 | - |
dc.publisher.place | Hong Kong | - |
dc.identifier.issnl | 2076-2275 | - |