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Nonlinear modulated waves near marginal state of instability
University of California.
Luleå tekniska universitet.
1993 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 47, p. 214-220Article in journal (Refereed) Published
Abstract [en]

We formulate a model equation for nonlinear modulated waves valid near the marginal state of instability. This equation we henceforth call the Extended Derivative Nonlinear Schrödinger equation (EDNLS). EDLNS has the same form as the Derivative Nonlinear Schrödinger equation (DNLS) except for a quintic nonlinear term which in special cases might be zero. EDNLS has three conservation laws which correspond to the first three of the conservation laws of the DNLS equation. We find the following criterion for modulational instability, k0 > -2a02σ. (Here k0, a0 and σ are the normalized background wavenumber and amplitude and the coefficient for the quintic term in the EDNLS equation.) In addition we classify the solitary and cnoidal waves for the EDNLS equation and study the nonlinear behavior of the modulational instability.

Place, publisher, year, edition, pages
1993. Vol. 47, p. 214-220
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-5838DOI: 10.1088/0031-8949/47/2/015ISI: A1993KR41600015Scopus ID: 2-s2.0-0027545808Local ID: 405d30e0-2bbf-11dd-8657-000ea68e967bOAI: oai:DiVA.org:ltu-5838DiVA, id: diva2:978714
Note
Godkänd; 1993; 20080527 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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