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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |