Stability of the NLS Equation with Viscosity Effect

被引：1

作者：

Karjanto, N. ^{[1
]}

Tiong, K. M. ^{[2
]}

机构：

[1] Sungkyunkwan Univ, Univ Coll, Dept Math, Suwon 440746, South Korea

[2] Univ Nottingham, Sch Business, Semenyih 43500, Selangor, Malaysia

来源：

JOURNAL OF APPLIED MATHEMATICS | 2011年

关键词：

NONLINEAR SCHRODINGER-EQUATION; KORTEWEG-DEVRIES EQUATION; ARBITRARY CROSS-SECTION; LONG GRAVITY-WAVES; MODULATIONAL INSTABILITY; WATER-WAVES; SOLITARY WAVES; DEEP-WATER; EVOLUTION; CHANNEL;

D O I：

10.1155/2011/863161

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonlinear Schrodinger (NLS) equation with an effect of viscosity is derived from a Kortewegde 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.

引用

页数：11

共 34 条

[1]

Agrawal G P., 2012, Nonlinear Fiber Optics

[2]

Akhmediev N., 1986, TEOR MAT FIZ, V69, P189

[3]

AKHMEDIEV NN, 1985, ZH EKSP TEOR FIZ+, V89, P1542

[4] DISINTEGRATION OF WAVE TRAINS ON DEEP WATER .1. THEORY [J].

BENJAMIN, TB ;

FEIR, JE .

JOURNAL OF FLUID MECHANICS, 1967, 27 :417-&

[5]

BRIDGES JT, 2007, PHYS FLUIDS, V19

[6]

Bronski JC, 2005, DYNAM PART DIFFER EQ, V2, P335

[7] RESONANT OSCILLATIONS OF WATER WAVES .I. THEORY [J].

CHESTER, W .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1968, 306 (1484) :5-&

[8] Matter-Wave Dark Solitons: Stochastic versus Analytical Results [J].

Cockburn, S. P. ;

Nistazakis, H. E. ;

Horikis, T. P. ;

Kevrekidis, P. G. ;

Proukakis, N. P. ;

Frantzeskakis, D. J. .

PHYSICAL REVIEW LETTERS, 2010, 104 (17)

[9] A KORTEWEG-DEVRIES EQUATION MODIFIED BY VISCOSITY FOR WAVES IN A CHANNEL OF UNIFORM BUT ARBITRARY CROSS-SECTION [J].

DAS, KP .

PHYSICS OF FLUIDS, 1985, 28 (03) :770-775

[10] THE KORTEWEG-DEVRIES EQUATION MODIFIED BY VISCOSITY FOR WAVES IN A 2-LAYER FLUID IN A CHANNEL OF ARBITRARY CROSS-SECTION [J].

DAS, KP ;

CHAKRABARTI, J .

PHYSICS OF FLUIDS, 1986, 29 (03) :661-666

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