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2011 Stability of the NLS Equation with Viscosity Effect
N. Karjanto, K. M. Tiong
J. Appl. Math. 2011: 1-11 (2011). DOI: 10.1155/2011/863161


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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N. Karjanto. K. M. Tiong. "Stability of the NLS Equation with Viscosity Effect." J. Appl. Math. 2011 1 - 11, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1216.35141
MathSciNet: MR2794076
Digital Object Identifier: 10.1155/2011/863161

Rights: Copyright © 2011 Hindawi


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