2009
DOI: 10.1143/jpsj.78.084001
|View full text |Cite
|
Sign up to set email alerts
|

Dissipative Solitons in Coupled Complex Ginzburg–Landau Equations

Abstract: Pulse propagation in inhomogeneous nonlinear media with linear and nonlinear gain and loss, described by a system of nonlinearly coupled complex Ginzburg-Landau equations (CGLEs) with variable coefficients, is considered. Exact solitary pulse (SP) solutions are obtained analytically, for special choices of variable coefficients of the nonlinear gain/loss terms, by a modified Hirota bilinear method. The solutions include space-or time-dependent wave numbers, which imply dilatation or compression of the SPs. Sta… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2

Citation Types

0
2
0

Year Published

2013
2013
2022
2022

Publication Types

Select...
5

Relationship

0
5

Authors

Journals

citations
Cited by 12 publications
(2 citation statements)
references
References 37 publications
0
2
0
Order By: Relevance
“…To describe the propagation of optical solitons in optical fibers, the nonlinear Schrödinger equation (NLSE) known as an important and universal model has been developed with some generalizations and soliton solutions presented [6][7][8][9][10][11][12][13]. Nevertheless, the generalized Ginzburg-Landau equation (GGLE), which is widely applied in such fields as superconductivity, liquid crystal, Bose-Einstein condensate, can be considered as a dissipative generalization of NLSE [14][15][16][17]. Different analytical and numerical methods have been applied to the GGLE, while various novel solutions including the pulsating, erupting and creeping solitons have been obtained [18][19][20][21][22][23].…”
Section: Introductionmentioning
confidence: 99%
“…To describe the propagation of optical solitons in optical fibers, the nonlinear Schrödinger equation (NLSE) known as an important and universal model has been developed with some generalizations and soliton solutions presented [6][7][8][9][10][11][12][13]. Nevertheless, the generalized Ginzburg-Landau equation (GGLE), which is widely applied in such fields as superconductivity, liquid crystal, Bose-Einstein condensate, can be considered as a dissipative generalization of NLSE [14][15][16][17]. Different analytical and numerical methods have been applied to the GGLE, while various novel solutions including the pulsating, erupting and creeping solitons have been obtained [18][19][20][21][22][23].…”
Section: Introductionmentioning
confidence: 99%
“…While the system with constant coefficients has been studied from different points of view by many researchers (see [2][3][4][5][6] and their references, only to cite some selected examples from a vast bibliography), the consideration of the CGLS or cCGLS with variable coefficients is more scarce [7][8][9]. For a single CGLE, [10] presents a complete analysis of equivalence transformations and Lie point symmetries.…”
Section: Introductionmentioning
confidence: 99%