Stability of the NLS Equation with Viscosity Effect

Stability of the NLS Equation with Viscosity Effect

A nonlinear Schrödinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In th...

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Main Authors: N. Karjanto, K. M. Tiong
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2011/863161
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spelling doaj-023614f4004a436abe76e61a921542902020-11-24T23:17:53ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/863161863161Stability of the NLS Equation with Viscosity EffectN. Karjanto0K. M. Tiong1Department of Mathematics, University College, Sungkyunkwan University, Natural Science Campus, Jangan-gu, Suwon, Gyeonggi-do 440-746, Republic of KoreaNottingham University Business School, The University of Nottingham Malaysia Campus, Jalan Broga, Semenyih 43500, Selangor, MalaysiaA nonlinear Schrödinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with viscosity is investigated. The corresponding modulational dispersion relation is expressed as a quadratic equation with complex-valued coefficients. By restricting the modulational wavenumber into the case of narrow-banded spectra, it is observed that a type of dissipation, in this case the effect of viscosity, stabilizes the modulational instability, as confirmed by earlier findings.http://dx.doi.org/10.1155/2011/863161
collection DOAJ
language English
format Article
sources DOAJ
author N. Karjanto
K. M. Tiong
spellingShingle N. Karjanto
K. M. Tiong
Stability of the NLS Equation with Viscosity Effect
Journal of Applied Mathematics
author_facet N. Karjanto
K. M. Tiong
author_sort N. Karjanto
title Stability of the NLS Equation with Viscosity Effect
title_short Stability of the NLS Equation with Viscosity Effect
title_full Stability of the NLS Equation with Viscosity Effect
title_fullStr Stability of the NLS Equation with Viscosity Effect
title_full_unstemmed Stability of the NLS Equation with Viscosity Effect
title_sort stability of the nls equation with viscosity effect
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2011-01-01
description A nonlinear Schrödinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time scale. It is well known that the plane-wave solution of the NLS equation exhibits modulational instability phenomenon. In this paper, the modulational instability of the plane-wave solution of the NLS equation modified with viscosity is investigated. The corresponding modulational dispersion relation is expressed as a quadratic equation with complex-valued coefficients. By restricting the modulational wavenumber into the case of narrow-banded spectra, it is observed that a type of dissipation, in this case the effect of viscosity, stabilizes the modulational instability, as confirmed by earlier findings.
url http://dx.doi.org/10.1155/2011/863161
work_keys_str_mv AT nkarjanto stabilityofthenlsequationwithviscosityeffect
AT kmtiong stabilityofthenlsequationwithviscosityeffect
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