Impact of higher-order effects on the dynamics of soliton solutions in the (3+1)D cubic-quintic-septic complex Ginzburg–Landau equation with higher-order dispersion terms

Djoko, Martin; Djazet, Alain; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin

doi:10.1016/j.ijleo.2023.170834

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…More explicitly Eq. (1) denotes a complex optical field u(z, t) traveling along z, where the first term in the right-hand side represents the group-velocity dispersion (δu tt ), the second term indicates the Kerr nonlinearity of the transparent material (−σ|u| 2 u), the third term accounts for both the plasma absorption and optical field defocusing (iγ(1 − iω 0 τ 0 )ρu) and the last quantity represents both K-photon absorption mechanism and the higher-order correction term to the nonlinear refractive index [25,26], in the optical Kerr medium (−(M 0 + iµ 0 )|u| 2K−2 u). Considering Eq.…”

Section: Mathematical Modelmentioning

confidence: 99%

Dynamics and stability of ultrashort laser in Kerr nonlinear optical materials: competing effects between K-photon absorption and the higher-order correction term to the nonlinear refractive index

Nteutse

Geletu

2023

Preprint

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Ultrashort laser micromachining is a versatile technology used in modern industries for manipulating transparent materials with precision. In these applications, laser systems are customized for specific power levels and wavelengths, requiring an understanding of different laser operation regimes to optimize their utilization, as well as technological advancement. This study proposes a theoretical analysis to investigate the impact of the competition between multiphoton absorption and the higher order correction term to the nonlinear refractive index on laser propagation and stability in Kerr nonlinear transparent materials. The study focuses on the mathematical model that includes a complex nonlinear K-order Ginzburg-Landau equation coupled to the Drude equation that captures the growth rate of the electron plasma density. Through global stability investigation, a diverse range of fixed points is revealed in the amplitude-frequency plane. An examination of the steady-state stability of these fixed point solutions reveals that, depending on the sign of the spatial noise, the combination of the multipho-ton absorption process with the higher-order correction term to the nonlinear refractive index can be detrimental or beneficial to the continuous-wave regime. According to numerical simulations of the mathematical model in the fully non-linear regime, we found that low values of the higher-order correction term to the nonlinear refractive index, denoted as M0 promote stable pulse trains patterns, mainly when the multiphoton absorption rate is high, whereas high values of M0 1 induced a train of anharmonic wave patterns as the multiphoton absorption rate gets stronger.

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Section: Mathematical Modelmentioning

confidence: 99%

Dynamics and stability of ultrashort laser in Kerr nonlinear optical materials: competing effects between K-photon absorption and the higher-order correction term to the nonlinear refractive index

Nteutse

Geletu

2023

Preprint

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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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Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach

Abbaszadeh,

Salec,

Aal-Ezirej

2023

Opt Quant Electron

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Impact of higher-order effects on the dynamics of soliton solutions in the (3+1)D cubic-quintic-septic complex Ginzburg–Landau equation with higher-order dispersion terms

Cited by 5 publications

References 36 publications

Dynamics and stability of ultrashort laser in Kerr nonlinear optical materials: competing effects between K-photon absorption and the higher-order correction term to the nonlinear refractive index

Dynamics and stability of ultrashort laser in Kerr nonlinear optical materials: competing effects between K-photon absorption and the higher-order correction term to the nonlinear refractive index

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

Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach

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