Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

Zhuravlev, M. N.; Ostrovskaya, N. V.

doi:10.1134/1.1800200

Cited by 14 publications

(7 citation statements)

References 3 publications

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“…The method was also used for the CGLE in [36,37,38], where simplified trial functions were considered. For special problems, even the first two equations (4) may be sufficient when we deal with specific two-dimensional reductions of the CGLE [39].…”

Section: The Methods Of Momentsmentioning

confidence: 99%

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Three Sources and Three Component Parts of the Concept of Dissipative Solitons

Akhmediev

Ankiewicz

2008

Lecture Notes in Physics

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We explain the notion of dissipative solitons within a historical perspective. We show that the ideas of the theory of dissipative solitons emerge from several fields, including classical soliton theory, nonlinear dynamics, with its theory of bifurcations, and Prigogine's concept of self-organization. A new notion, emerging from this three-part foundation, allows us to build the novel concept of the dissipative soliton. We also show that reductions to lower dimensional systems have to be done carefully and should always include a comparison of the results with numerical simulations of the original equations.

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Section: The Methods Of Momentsmentioning

confidence: 99%

“…The phase in (5) is expanded up to the second order. This form differs from the trial function used in [36], where only linear terms in the phase were considered. We emphasize that the chirp is highly important for solutions of the CGLE.…”

Section: Trial Function: Sech-pulsementioning

confidence: 99%

Three Sources and Three Component Parts of the Concept of Dissipative Solitons

Akhmediev

Ankiewicz

2008

Lecture Notes in Physics

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“…Hence, this optimization requires a lot of computer time. Analytical methods reducing the number of degrees of freedom in the system [17] may help in attempts to find a more regular technique to narrow the range of the parameter set. However, even with the reductions, direct numerical simulations cannot be eliminated.…”

Section: Laser Model With Parameter Managementmentioning

confidence: 99%

Dissipative soliton interactions inside a fiber laser cavity

Akhmediev¹,

Soto-Crespo

Grapinet

et al. 2005

Optical Fiber Technology

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“…However, there has been significant effort within the mode-locked laser community to study analogous driven and damped systems. Works on dissipation terms and saturation [38][39][40][41], the study of dissipative solitons dynamics [42][43][44][45][46] and other numerical studies of the cubic quintic complex Ginzburg-Landau equation [47,48] are highly relevant to the development of a driven damped model for spin waves in magnetic thin films. These works explore the dynamics of solitary waves and their associated wave equations under the influences of gain and loss.…”

Section: Introductionmentioning

confidence: 99%

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Anderson

Ryan

et al. 2014

New J. Phys.

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A numerical exploration of a gain-loss nonlinear Schrödinger equation was carried out utilizing over 180 000 core hours to conduct more than 10 000 unique simulations in an effort to characterize the model's six dimensional parameter space. The study treated the problem in full generality, spanning a minimum of eight orders of magnitude for each of three linear and nonlinear gain terms and five orders of magnitude for higher order nonlinearities. The gain-loss nonlinear Schrödinger equation is of interest as a model for spin wave envelopes in magnetic thin film active feedback rings and analogous driven damped nonlinear physical systems. Bright soliton trains were spontaneously driven out of equilibrium and behaviors stable for tens of thousands of round trip times were numerically identified. Nine distinct complex dynamical behaviors with lifetimes on the order of ms were isolated as part of six identified solution classes. Numerically located dynamical behaviors include: (i) low dimensional chaotic modulations of bright soliton trains; (ii) spatially symmetric/asymmetric interactions of solitary wave peaks; (iii) dynamical pattern formation and recurrence; (iv) steady state solutions; and

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Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

Cited by 14 publications

References 3 publications

Three Sources and Three Component Parts of the Concept of Dissipative Solitons

Three Sources and Three Component Parts of the Concept of Dissipative Solitons

Dissipative soliton interactions inside a fiber laser cavity

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

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