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Analytic solutions for the generalized complex Ginzburgâ€“Landau equation in fiber lasers

Nonlinear dynamics, ISSN 0924-090X, 9/2017, Volume 89, Issue 4, pp. 2933 - 2939

Generalized complex Ginzburgâ€“Landau equation (GCGLE) can be used to describe the nonlinear dynamic characteristics of fiber lasers and has riveted much attention of researchers in ultrafast optics...

Engineering | Vibration, Dynamical Systems, Control | Generalized complex Ginzburgâ€“Landau equation | Classical Mechanics | Soliton | Automotive Engineering | Mechanical Engineering | Modified Hirota method | Symbolic computation | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Lasers | Equipment and supplies | Fiber optics | Dynamic characteristics | Nonlinear dynamics | Parameters | Mathematical analysis | Exact solutions | Nonlinearity | Fiber lasers

Engineering | Vibration, Dynamical Systems, Control | Generalized complex Ginzburgâ€“Landau equation | Classical Mechanics | Soliton | Automotive Engineering | Mechanical Engineering | Modified Hirota method | Symbolic computation | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Lasers | Equipment and supplies | Fiber optics | Dynamic characteristics | Nonlinear dynamics | Parameters | Mathematical analysis | Exact solutions | Nonlinearity | Fiber lasers

Journal Article

Journal of computational physics, ISSN 0021-9991, 05/2016, Volume 312, pp. 31 - 49

...â€“Landau equation involving fractional Laplacian. The scheme is based on the implicit midpoint rule for the temporal discretization and a weighted and shifted...

Fractional Laplacian | Weighted and shifted GrÃ¼nwald difference | Riesz fractional derivative | Fractional Ginzburgâ€“Landau equation | Convergence | Fractional Ginzburg-Landau equation | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Operators | Discretization | Mathematical analysis | Inequalities | Norms | Mathematical models | Optimization | Mathematics - Numerical Analysis

Fractional Laplacian | Weighted and shifted GrÃ¼nwald difference | Riesz fractional derivative | Fractional Ginzburgâ€“Landau equation | Convergence | Fractional Ginzburg-Landau equation | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Operators | Discretization | Mathematical analysis | Inequalities | Norms | Mathematical models | Optimization | Mathematics - Numerical Analysis

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2013, Volume 45, Issue 1, pp. 14 - 30

.... This leads to a slow modulation of the dominant pattern. Here we consider the stochastic SwiftHohenberg equation and derive rigorously the Ginzburg-Landau equation as a modulation equation for the amplitudes of the dominating modes...

Additive noise | Ginzburg-Landau equation | Swift-Hohenberg equation | Stabilization by noise | Modulation equation | Multiscale analysis | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Amplitudes | Stability | Partial differential equations | Mathematical analysis | Noise | Modulation | Stochasticity

Additive noise | Ginzburg-Landau equation | Swift-Hohenberg equation | Stabilization by noise | Modulation equation | Multiscale analysis | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Amplitudes | Stability | Partial differential equations | Mathematical analysis | Noise | Modulation | Stochasticity

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 11/2013, Volume 76, Issue 1, pp. 441 - 445

...) equation to describe the transition and critical phenomenon in traffic flow by applying the reductive perturbation method...

Engineering | Vibration, Dynamical Systems, Control | Lattice hydrodynamic model | Traffic flow | Time-dependent Ginzburgâ€“Landau equation | Mechanics | Automotive Engineering | Mechanical Engineering | Time-dependent Ginzburg-Landau equation | Technology | Engineering, Mechanical | Science & Technology | Time dependence | Mathematical models | Perturbation methods | Computer simulation | Delay | Computational fluid dynamics | Mathematical analysis | Lattices | Fluid flow | Hydrodynamics

Engineering | Vibration, Dynamical Systems, Control | Lattice hydrodynamic model | Traffic flow | Time-dependent Ginzburgâ€“Landau equation | Mechanics | Automotive Engineering | Mechanical Engineering | Time-dependent Ginzburg-Landau equation | Technology | Engineering, Mechanical | Science & Technology | Time dependence | Mathematical models | Perturbation methods | Computer simulation | Delay | Computational fluid dynamics | Mathematical analysis | Lattices | Fluid flow | Hydrodynamics

Journal Article

Nonlinear dynamics, ISSN 0924-090X, 12/2018, Volume 94, Issue 4, pp. 2363 - 2371

...Nonlinear Dyn (2018) 94:2363â€“2371 https://doi.org/10.1007/s11071-018-4494-5 ORIGINAL PAPER Optical vortices in the Ginzburgâ€“Landau equation with cubicâ€“quintic...

Ginzburgâ€“Landau equation | Optical vortices | Cubicâ€“quintic nonlinearity | Mechanics | Engineering | Technology | Engineering, Mechanical | Science & Technology | Electron beams | Initial conditions | Computer simulation | Propagation | Energy dissipation | Vortices | Evolution | Nonlinearity | Topology | Beads

Ginzburgâ€“Landau equation | Optical vortices | Cubicâ€“quintic nonlinearity | Mechanics | Engineering | Technology | Engineering, Mechanical | Science & Technology | Electron beams | Initial conditions | Computer simulation | Propagation | Energy dissipation | Vortices | Evolution | Nonlinearity | Topology | Beads

Journal Article

Physica A, ISSN 0378-4371, 08/2005, Volume 354, Issue 1-4, pp. 249 - 261

We derive the fractional generalization of the Ginzburgâ€“Landau equation from the variational Euler...

Ginzburgâ€“Landau equation | Fractional derivatives and integrals fractal medium | Fractional equation | Ginzburg-Landau equation | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology

Ginzburgâ€“Landau equation | Fractional derivatives and integrals fractal medium | Fractional equation | Ginzburg-Landau equation | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology

Journal Article

Optics communications, ISSN 0030-4018, 06/2018, Volume 416, pp. 190 - 201

...â€“Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links...

SSFM | Stationary and pulsating optical bullets | Solitons | Bell-shaped | Generalized-Gaussian beam | Nonlinearities | Diffraction | Raman effect | Self-steepening | Vortex dissipative light bullets | RK4 | Sith-order dispersion term | Complex Ginzburgâ€“Landau equation | Optics | Physical Sciences | Science & Technology

SSFM | Stationary and pulsating optical bullets | Solitons | Bell-shaped | Generalized-Gaussian beam | Nonlinearities | Diffraction | Raman effect | Self-steepening | Vortex dissipative light bullets | RK4 | Sith-order dispersion term | Complex Ginzburgâ€“Landau equation | Optics | Physical Sciences | Science & Technology

Journal Article

Modern physics letters A, ISSN 1793-6632, 02/2019, Volume 34, Issue 3, p. 1950019

...â€“Landau equation with Kerr law of nonlinearity. Meanwhile, the interaction between rational solutions and the kink wave is also investigated...

Rational solutions | logarithmic transformations | multi-waves interactions | complex Ginzburg-Landau equation | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics, Mathematical | Physics | Science & Technology

Rational solutions | logarithmic transformations | multi-waves interactions | complex Ginzburg-Landau equation | Physical Sciences | Physics, Nuclear | Astronomy & Astrophysics | Physics, Particles & Fields | Physics, Mathematical | Physics | Science & Technology

Journal Article

Nonlinear dynamics, ISSN 0924-090X, 12/2017, Volume 90, Issue 4, pp. 2745 - 2753

Spiral dynamics in the complex Ginzburgâ€“Landau equationÂ (CGLE) with a feedback control are studied...

Chaos | Engineering | Vibration, Dynamical Systems, Control | Ginzburgâ€“Landau equation | Classical Mechanics | Automotive Engineering | Spiral wave | Tip | Mechanical Engineering | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Parameters | Position measurement | Control systems | Drift | Feedback loops | Control theory | Feedback control | Positive feedback | Time lag

Chaos | Engineering | Vibration, Dynamical Systems, Control | Ginzburgâ€“Landau equation | Classical Mechanics | Automotive Engineering | Spiral wave | Tip | Mechanical Engineering | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Parameters | Position measurement | Control systems | Drift | Feedback loops | Control theory | Feedback control | Positive feedback | Time lag

Journal Article

Fractional calculus & applied analysis, ISSN 1311-0454, 3/2013, Volume 16, Issue 1, pp. 226 - 242

The well-posedness for the Cauchy problem of the nonlinear fractional SchrÃ¶dinger equation
$u_t + i( - \Delta )^\alpha u + i|u|^2 u = 0,(x,t) \in \mathbb{R}^n...

Abstract Harmonic Analysis | fractional SchrÃ¶dinger equation | Functional Analysis | Primary 26A33 | well-posedness | Analysis | Secondary 35E15, 35Q55 | Mathematics | fractional Ginzburg-Landau equation | Integral Transforms, Operational Calculus | inviscid limit behavior | Mathematics, Interdisciplinary Applications | Physical Sciences | Mathematics, Applied | Science & Technology

Abstract Harmonic Analysis | fractional SchrÃ¶dinger equation | Functional Analysis | Primary 26A33 | well-posedness | Analysis | Secondary 35E15, 35Q55 | Mathematics | fractional Ginzburg-Landau equation | Integral Transforms, Operational Calculus | inviscid limit behavior | Mathematics, Interdisciplinary Applications | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

Optik (Stuttgart), ISSN 0030-4026, 07/2018, Volume 164, pp. 210 - 217

The main object of this paper is to construct the new exact solutions of a nonlinear evolution equation that appears in mathematical physics, specifically complex cubic-quintic Ginzburg...

Nonlinear partial differential equations | Complex cubic-quintic Ginzburgâ€“Landau Equation | First integral method | Exact solutions | Optics | Physical Sciences | Science & Technology

Nonlinear partial differential equations | Complex cubic-quintic Ginzburgâ€“Landau Equation | First integral method | Exact solutions | Optics | Physical Sciences | Science & Technology

Journal Article

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Ergodicity of the stochastic real Ginzburgâ€“Landau equation driven by Î±-stable noises

Stochastic processes and their applications, ISSN 0304-4149, 10/2013, Volume 123, Issue 10, pp. 3710 - 3736

We study the ergodicity of the stochastic real Ginzburgâ€“Landau equation driven by additive Î±...

Stochastic real Ginzburgâ€“Landau equation driven by [formula omitted]-stable noises | Strong Feller property | Galerkin approximation | Accessibility | Ergodicity | Maximal inequality | Stochastic [formula omitted]-stable convolution | Stochastic Î±-stable convolution | Stochastic real Ginzburg-Landau equation driven by Î±-stable noises | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Stochastic real Ginzburgâ€“Landau equation driven by [formula omitted]-stable noises | Strong Feller property | Galerkin approximation | Accessibility | Ergodicity | Maximal inequality | Stochastic [formula omitted]-stable convolution | Stochastic Î±-stable convolution | Stochastic real Ginzburg-Landau equation driven by Î±-stable noises | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Journal Article

Physica. B, Condensed matter, ISSN 0921-4526, 11/2016, Volume 500, pp. 142 - 153

Within the continuum thermodynamic framework, we derive the evolution equation for the magnetization vector in a ferromagnetic body...

Thermodynamics | Paramagneticâ€“ferromagnetic transition | Temperature-dependent magnetic susceptibility | Landauâ€“Lifshitzâ€“Bloch equation | Ginzburgâ€“Landau theory | Physics, Condensed Matter | Physical Sciences | Physics | Science & Technology | Ferromagnetism | Magnetization | Magnetic fields | Anisotropy | Analysis

Thermodynamics | Paramagneticâ€“ferromagnetic transition | Temperature-dependent magnetic susceptibility | Landauâ€“Lifshitzâ€“Bloch equation | Ginzburgâ€“Landau theory | Physics, Condensed Matter | Physical Sciences | Physics | Science & Technology | Ferromagnetism | Magnetization | Magnetic fields | Anisotropy | Analysis

Journal Article

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New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity

Optik (Stuttgart), ISSN 0030-4026, 08/2018, Volume 167, pp. 218 - 227

In this paper, we find new solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity according to the new extended direct algebraic method...

Ginzburg-Landau equation with Kerr law nonlinearity | Solitons solutions | The new extended direct algebraic method | Optics | Physical Sciences | Science & Technology

Ginzburg-Landau equation with Kerr law nonlinearity | Solitons solutions | The new extended direct algebraic method | Optics | Physical Sciences | Science & Technology

Journal Article