2007
DOI: 10.1016/j.yofte.2006.12.001
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Dissipative solitons with a Lagrangian approach

Abstract: We apply Lagrangian techniques to dissipative systems described by the complex Ginzburg-Landau equation (CGLE) that is used for modeling passively mode-locked fiber lasers and all-optical soliton transmission lines. In particular, using Lagrangian equations, we re-derive the known exact solutions of the CGLE. We also apply the technique to finding approximate solutions for pulsating solitons.

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Cited by 50 publications
(30 citation statements)
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References 21 publications
(31 reference statements)
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“…The phase factor is accounted for in the θ term and, as shown below, can predict the observed behavior of the solutions to a reasonable extent. The standard variational approach for systems with dissipative terms can be modified as [43,45] d dz…”
Section: Variational Approachmentioning
confidence: 99%
“…The phase factor is accounted for in the θ term and, as shown below, can predict the observed behavior of the solutions to a reasonable extent. The standard variational approach for systems with dissipative terms can be modified as [43,45] d dz…”
Section: Variational Approachmentioning
confidence: 99%
“…The effect of dissipative factors can be taken into account using the Ritz-Kantorovich method [51][52][53][54] when the reduced Euler-Lagrange equations are driven by a dissipative "source" [52]:…”
Section: Perfectly Saturable Absorbermentioning
confidence: 99%
“…The most famous and studied one is based on the complex nonlinear Ginzburg-Landau equation which can be treated as a dissipative extension of the nonlinear Schrödinger equation [45]. 2 A very productive approach to the study of this class of equations is based on the so-called variational approximation (VA) [49][50][51]. The non-dissipative effects can be described by the Lagrangian density:…”
Section: Introductionmentioning
confidence: 99%
“…Most powerful approaches to the theory of DSs have been developed in the framework of approximated techniques (for review see [44]): AM [165,167,[217][218][219][220][221], VA [77,177,[222][223][224]225] and MM [175,210,222,226]. The most impressive results obtained are: (i) physically relevant representation of DS parametric space was revealed (it is a so-called master diagram, see [44] for review and Figure 10); (ii) such a representation allows understanding the structural properties of DS and its energy-scaling laws (i.e.…”
Section: Fiber Lasermentioning
confidence: 99%