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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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/863161 |
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| author | N. Karjanto K. M. Tiong |
| author_facet | N. Karjanto K. M. Tiong |
| author_sort | N. Karjanto |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-023614f4004a436abe76e61a92154290 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-023614f4004a436abe76e61a921542902025-02-03T06:07:22ZengWileyJournal 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 |
| spellingShingle | N. Karjanto K. M. Tiong Stability of the NLS Equation with Viscosity Effect Journal of Applied Mathematics |
| title | 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_short | Stability of the NLS Equation with Viscosity Effect |
| title_sort | stability of the nls equation with viscosity effect |
| url | http://dx.doi.org/10.1155/2011/863161 |
| work_keys_str_mv | AT nkarjanto stabilityofthenlsequationwithviscosityeffect AT kmtiong stabilityofthenlsequationwithviscosityeffect |