Perturbations of dark solitons

被引：37

作者：

Ablowitz, M. J. ^{[1
]}

Nixon, S. D. ^{[1
]}

Horikis, T. P. ^{[2
]}

Frantzeskakis, D. J. ^{[3
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] Univ Ioannina, Dept Math, GR-45110 Ioannina, Greece

[3] Univ Athens, Dept Phys, Athens 15784, Greece

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2011年 / 467卷 / 2133期

基金：

美国国家科学基金会;

关键词：

perturbation theory; solitons; optics; SQUARED JOST SOLUTIONS; OPTICAL FIBERS; COMPLETE SET; PROPAGATION; DYNAMICS;

D O I：

10.1098/rspa.2010.0663

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A direct perturbation method for approximating dark soliton solutions of the nonlinear Schrodinger (NLS) equation under the influence of perturbations is presented. The problem is broken into an inner region, where the core of the soliton resides, and an outer region, which evolves independently of the soliton. It is shown that a shelf develops around the soliton that propagates with speed determined by the background intensity. Integral relations obtained from the conservation laws of the NLS equation are used to determine the properties of the shelf. The analysis is developed for both constant and slowly evolving backgrounds. A number of problems are investigated, including linear and nonlinear damping type perturbations.

引用

页码：2597 / 2621

页数：25

共 23 条

[1] Ablowitz M., 1981, SOLITONS INVERSE SCA, DOI [10.1137/1.9781611970883, DOI 10.1137/1.9781611970883]
[2] Asymptotic Analysis of Pulse Dynamics in Mode-Locked Lasers
Ablowitz, Mark J.
Horikis, Theodoros P.
Nixon, Sean D.
Zhu, Yi
[J]. STUDIES IN APPLIED MATHEMATICS, 2009, 122 (04) : 411 - 425
[3] Abramowitz M., 1964, HDB MATH FUNCTIONS, V55
[4] A perturbation method for dark solitons based on a complete set of the squared Jost solutions
Ao, SM
Yan, JR
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (11): : 2399 - 2413
[5] Nonadiabatic dynamics of dark solitons
Burtsev, S
Camassa, R
[J]. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 1997, 14 (07) : 1782 - 1787
[6] A direct perturbation theory for dark solitons based on a complete set of the squared Jost solutions
Chen, XJ
Chen, ZD
Huang, NN
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (33): : 6929 - 6947
[7] PICOSECOND STEPS AND DARK PULSES THROUGH NONLINEAR SINGLE-MODE FIBERS
EMPLIT, P
HAMAIDE, JP
REYNAUD, F
FROEHLY, C
BARTHELEMY, A
[J]. OPTICS COMMUNICATIONS, 1987, 62 (06) : 374 - 379
[8] THE PROPAGATION OF BRIGHT AND DARK SOLITONS IN LOSSY OPTICAL FIBERS
GIANNINI, JA
JOSEPH, RI
[J]. IEEE JOURNAL OF QUANTUM ELECTRONICS, 1990, 26 (12) : 2109 - 2114
[9] A DIRECT APPROACH TO STUDYING SOLITON PERTURBATIONS
HERMAN, RL
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (12): : 2327 - 2362
[10] KARPMAN VI, 1977, ZH EKSP TEOR FIZ+, V73, P537

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