Cubic quintic Ginzburg Landau equation as a model for resonant interaction of EM field with nonlinear media

Aleksić, Branislav N.; Uvarova, L. A.; Aleksić, Najdan B.; Belić, Milivoj R.

doi:10.1007/s11082-020-02271-2

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…Inserting equation (9) into equation (8), combining all power coefficients of f(η) and making their results to zero, p i (t), q i (t) and b i (t) can be gotten. Through solving the auxiliary equations in equation (9), the solutions of equation (8) can be given.…”

Section: The Improved Unified Methodsmentioning

confidence: 99%

“…We consider p = 2 to construct the soliton wave solutions. From equation (9), we assume that it can be expanded as follows…”

Section: Soliton Wave Solutionsmentioning

confidence: 99%

“…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%

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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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Section: The Improved Unified Methodsmentioning

confidence: 99%

“…We consider p = 2 to construct the soliton wave solutions. From equation (9), we assume that it can be expanded as follows…”

Section: Soliton Wave Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Due to the fact that the operator � it can have n proper functions and n corresponding energy values , if they coincide, we get degenerate States, and if there are many continuous values, a continuous spectrum is formed. The stable position of any particle is considered to be the state of equilibrium or when the particle has the lowest energy reserve 1 [9][10][11][12][13][14].…”

Section: Methods Of Researchmentioning

confidence: 99%

Simulation of the Processing Process in a Glow Discharge Plasma Generator

Logvin

Yvarova

2021

EPJ Web Conf.

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A theory has been developed that explains the structure formation in a thin surface layer of a material after low-energy exposure to a glow discharge plasma. This makes it possible to design new methods, technologies and automated devices for the development of an automated technological environment for strengthening various types of tools from various materials. Based on the developed theory, a self-learning system with a developing database was created for monitoring all stages of processing in a glow discharge plasma generator. Any crystal structure can be classified as a complex nonlinear system. When studying the dynamic response of such systems to an external low-energy effect, it was shown that by the time when the nonlinear vibrations stop, the atoms of the crystal lattice are stabilized in new positions. Based on the purpose of the products to be processed in the glow discharge plasma generator, with taking into account their operating conditions, it is possible to increase their production life up to 2 times or more. These technologies should be used at the final stage of the production process because they do not lead to distortion of the shape and size of the working surfaces of products being manufactured. In this case, the residual stresses are redistributed in the surface layer of the material with the formation of an equal structure that improves the running-in conditions of mating parts of devices and mechanisms. For cutting and forming tools, the run-in stage is reduced to the stage of uniform wear.

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“…As shown in paper (Aleksić et al 2020) under these conditions for function G, it is possible to obtain a good approximation using a second order polynomial where Considering Eqs. ( 8)-( 10), Eq.…”

Section: Modelmentioning

confidence: 96%

Dissipative structures in the resonant interaction of laser radiation with nonlinear dispersive medium

2021

Self Cite

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The article presents the results of studies on the stability of dissipative structures (DS) arising in the resonant interaction of laser radiation with a nonlinear medium. Resonant interaction is modeled by the one dimensional complex Ginzburg-Landau equation with a nonconservative cubic–quintic nonlinearity. The areas of existence of stable DS solutions have been determined analytically using a variational approach and confirmed numerically by extensive numerical simulations.

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Cubic quintic Ginzburg Landau equation as a model for resonant interaction of EM field with nonlinear media

Cited by 8 publications

References 22 publications

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

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

Simulation of the Processing Process in a Glow Discharge Plasma Generator

Dissipative structures in the resonant interaction of laser radiation with nonlinear dispersive medium

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