Femtosecond solitons and double-kink solitons in passively mode-locked lasers

Kengne, Emmanuel; Lakhssassi, Ahmed

doi:10.1007/s11082-023-04854-1

Cited by 6 publications

(1 citation statement)

References 51 publications

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“…The complex Ginzburg-Landau equation is a typical model of weakly nonlinear dissipative systems and one of the most studied nonlinear equations in physics, which can be used to describe a wide variety of nonlinear phenomena, such as nonlinear photonics, dynamic phase changes, superconductivity, superfluid, fluid dynamics, plasma, Bose-Einstein condensation, liquid crystals, field theory strings and so on [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In its most basic forms, the complex Ginzburg-Landau equation includes the cubic nonlinearity [1] and has the following form [3] (…”

Section: Introductionmentioning

confidence: 99%

Exact solutions to the fractional complex Ginzburg-Landau equation with cubic-quintic and Kerr law nonlinearities

Yang,

Gao

2024

Phys. Scr.

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The fractional complex cubic-quintic Ginzburg-Landau equation (FCCQGLE) with variable coefficients is a propagation model of optical pulses in optical fibers, the quintic term contained in it not only explains the physical significances that are not found in the existing models, but also has more abundant dynamic characteristics compared with lower dimensional systems. In this paper, the exact solutions of this equation are obtained via the appropriate transformations methods, which also are divided into different kinds. More precisely, we acquire the solitary, soliton and elliptic waves solutions by using the improved unified method, the bright and dark solitons solutions by using the improved F-expansion method, as well as the traveling wave solutions through the improved ( G ′ / G 2 ) -expansion and Bernoulli sub-equation function methods. Furthermore, we draw the 3D, 2D, density and contour plots to understand the propagation forms and the changes of amplitudes, frequencies and shapes of the solutions for the FCCQGLE with variable coefficients. The last thing worth mentioning is that the improved unified method here extends the degree of the polynomial from n to -n in the hypothetical solutions, which is not appeared before.

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