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Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers

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

Generalized complex Ginzburg–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 Ginzburg–Landau equation | Classical Mechanics | Soliton | Automotive Engineering | Mechanical Engineering | Modified Hirota method | Symbolic computation | IMPACT | STATES | MECHANICS | OSCILLATORS | STABILITY | SCHRODINGER-EQUATION | Generalized complex Ginzburg-Landau equation | ENGINEERING, MECHANICAL | 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 Ginzburg–Landau equation | Classical Mechanics | Soliton | Automotive Engineering | Mechanical Engineering | Modified Hirota method | Symbolic computation | IMPACT | STATES | MECHANICS | OSCILLATORS | STABILITY | SCHRODINGER-EQUATION | Generalized complex Ginzburg-Landau equation | ENGINEERING, MECHANICAL | Lasers | Equipment and supplies | Fiber optics | Dynamic characteristics | Nonlinear dynamics | Parameters | Mathematical analysis | Exact solutions | Nonlinearity | Fiber lasers

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2018, Volume 41, pp. 607 - 641

The initial-dynamic boundary value problem (idbvp) for the complex Ginzburg–Landau equation (CGLE) on bounded domains of RN is studied by converting the given mathematical model into a Wentzell initial...

Complex Ginzburg–Landau equations | Inviscid limits | Dynamic boundary conditions | WEAK | MATHEMATICS, APPLIED | Complex Ginzburg-Landau equations | NONLINEAR SCHRODINGER-EQUATIONS | LOCAL SPACES | STABILIZATION | UNIFORM DECAY-RATES | CAUCHY-PROBLEM | WELL-POSEDNESS | MODEL

Complex Ginzburg–Landau equations | Inviscid limits | Dynamic boundary conditions | WEAK | MATHEMATICS, APPLIED | Complex Ginzburg-Landau equations | NONLINEAR SCHRODINGER-EQUATIONS | LOCAL SPACES | STABILIZATION | UNIFORM DECAY-RATES | CAUCHY-PROBLEM | WELL-POSEDNESS | MODEL

Journal Article

Nonlinear dynamics, ISSN 0924-090X, 2019, Volume 97, Issue 1, pp. 151 - 159

.... We derive simple analytic conditions for the onset of amplitude death of one macroscopic wavefunction in a system of two coupled complex Ginzburg-Landau equations with general nonlinear self...

STABILITY | SPATIOTEMPORAL CHAOS | MODE-LOCKING | Amplitude death | ENGINEERING, MECHANICAL | FIBERS | WAVES | MECHANICS | SOLITONS | Asymmetry | BOUNDS | Cross-phase modulation | Coupled complex Ginzburg-Landau systems | EQUATION | Thermodynamics | Lasers | Numerical analysis | Collapse | Nonlinear equations | Amplitudes | Computer simulation | Solid state lasers | Analog circuits | Death | Wave functions | Oscillators

STABILITY | SPATIOTEMPORAL CHAOS | MODE-LOCKING | Amplitude death | ENGINEERING, MECHANICAL | FIBERS | WAVES | MECHANICS | SOLITONS | Asymmetry | BOUNDS | Cross-phase modulation | Coupled complex Ginzburg-Landau systems | EQUATION | Thermodynamics | Lasers | Numerical analysis | Collapse | Nonlinear equations | Amplitudes | Computer simulation | Solid state lasers | Analog circuits | Death | Wave functions | Oscillators

Journal Article

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

...–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 Ginzburg–Landau equation | VARIATIONAL PRINCIPLE | MAXWELL EQUATIONS | LIGHT BULLETS | FIBERS | Complex Ginzburg-Landau equation | OPTICS | FEMTOSECOND ELECTROMAGNETIC SOLITONS | SCATTERING | DIRECT TIME INTEGRATION

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 Ginzburg–Landau equation | VARIATIONAL PRINCIPLE | MAXWELL EQUATIONS | LIGHT BULLETS | FIBERS | Complex Ginzburg-Landau equation | OPTICS | FEMTOSECOND ELECTROMAGNETIC SOLITONS | SCATTERING | DIRECT TIME INTEGRATION

Journal Article

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

...–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 | SCHRODINGER-EQUATION | PHYSICS, NUCLEAR | OPTICAL SOLITONS | PHYSICS, MATHEMATICAL | LUMP | SOLITON-SOLUTIONS | HIGHER-ORDER | ASTRONOMY & ASTROPHYSICS | BRIGHT | PHYSICS, PARTICLES & FIELDS

Rational solutions | logarithmic transformations | multi-waves interactions | complex Ginzburg-Landau equation | SCHRODINGER-EQUATION | PHYSICS, NUCLEAR | OPTICAL SOLITONS | PHYSICS, MATHEMATICAL | LUMP | SOLITON-SOLUTIONS | HIGHER-ORDER | ASTRONOMY & ASTROPHYSICS | BRIGHT | PHYSICS, PARTICLES & FIELDS

Journal Article

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On the solitary wave dynamics of complex Ginzburg–Landau equation with cubic nonlinearity

Optical and Quantum Electronics, ISSN 0306-8919, 4/2017, Volume 49, Issue 4, pp. 1 - 9

The complex Ginzburg–Landau equation with cubic nonlinearity is an ubiquitous model for the evolution of slowly varying wave packets in nonlinear dissipative media...

Nonlinear partial differential equations | First integral method | Optics, Lasers, Photonics, Optical Devices | Exact solutions | Characterization and Evaluation of Materials | (\frac{G'}{G})$$ ( G ′ G ) -Expansion | Computer Communication Networks | The complex Ginzburg–Landau equation | Physics | Electrical Engineering | (G′/G)-Expansion | (G'/G)-EXPANSION METHOD | The complex Ginzburg-Landau equation | TANH METHOD | (G'/G)-Expansion | EVOLUTION-EQUATIONS | OPTICS | PULSES | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Differential equations

Nonlinear partial differential equations | First integral method | Optics, Lasers, Photonics, Optical Devices | Exact solutions | Characterization and Evaluation of Materials | (\frac{G'}{G})$$ ( G ′ G ) -Expansion | Computer Communication Networks | The complex Ginzburg–Landau equation | Physics | Electrical Engineering | (G′/G)-Expansion | (G'/G)-EXPANSION METHOD | The complex Ginzburg-Landau equation | TANH METHOD | (G'/G)-Expansion | EVOLUTION-EQUATIONS | OPTICS | PULSES | ENGINEERING, ELECTRICAL & ELECTRONIC | Analysis | Differential equations

Journal Article

Optik, ISSN 0030-4026, 04/2018, Volume 158, pp. 368 - 375

This paper studies the complex Ginzburg–Landau equation (CGLE) which models soliton propagation in the presence of detuning factor in nonlinear optics...

Kerr law | Parabolic law | Quadratic–cubic law | Sine-Gordon equation method | Optical solitons | Complex Ginzburg–Landau equation | Quadratic-cubic law | SHRODINGERS EQUATION | MODULATION INSTABILITY ANALYSIS | SCHRODINGER-EQUATION | WAVE SOLUTIONS | SPATIALLY-DEPENDENT COEFFICIENTS | 1ST INTEGRAL METHOD | Complex Ginzburg-Landau equation | CONSERVATION-LAWS | RICCATI EQUATION | OPTICS | SPATIOTEMPORAL DISPERSION | BRIGHT

Kerr law | Parabolic law | Quadratic–cubic law | Sine-Gordon equation method | Optical solitons | Complex Ginzburg–Landau equation | Quadratic-cubic law | SHRODINGERS EQUATION | MODULATION INSTABILITY ANALYSIS | SCHRODINGER-EQUATION | WAVE SOLUTIONS | SPATIALLY-DEPENDENT COEFFICIENTS | 1ST INTEGRAL METHOD | Complex Ginzburg-Landau equation | CONSERVATION-LAWS | RICCATI EQUATION | OPTICS | SPATIOTEMPORAL DISPERSION | BRIGHT

Journal Article

Optik, 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 Ginzburg–Landau Equation | First integral method | Exact solutions | PERTURBATION | Equation | DARK | OPTICAL SOLITONS | FIBERS | TRAVELING-WAVE SOLUTIONS | Complex cubic-quintic Ginzburg-Landau | KERR | OPTICS | SPATIOTEMPORAL DISPERSION | NONLINEAR EVOLUTION-EQUATIONS

Nonlinear partial differential equations | Complex cubic-quintic Ginzburg–Landau Equation | First integral method | Exact solutions | PERTURBATION | Equation | DARK | OPTICAL SOLITONS | FIBERS | TRAVELING-WAVE SOLUTIONS | Complex cubic-quintic Ginzburg-Landau | KERR | OPTICS | SPATIOTEMPORAL DISPERSION | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 3/2017, Volume 350, Issue 2, pp. 507 - 568

We study a class of solutions to the parabolic Ginzburg–Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | HARMONIC MAPS | LOCAL SPACES | VORTICES | MEAN-CURVATURE | DYNAMICS | CAUCHY-PROBLEM | CONVERGENCE | VORTEX COLLISIONS | HEAT-FLOW | PHYSICS, MATHEMATICAL | DISSIPATION RATES | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | HARMONIC MAPS | LOCAL SPACES | VORTICES | MEAN-CURVATURE | DYNAMICS | CAUCHY-PROBLEM | CONVERGENCE | VORTEX COLLISIONS | HEAT-FLOW | PHYSICS, MATHEMATICAL | DISSIPATION RATES | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

EPL, ISSN 0295-5075, 11/2019, Volume 128, Issue 3, p. 30006

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear...

PHYSICS, MULTIDISCIPLINARY | EQUILIBRIUM DYNAMICS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | aging | pattern formation | complex Ginzburg-Landau equation | dynamic scaling

PHYSICS, MULTIDISCIPLINARY | EQUILIBRIUM DYNAMICS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | aging | pattern formation | complex Ginzburg-Landau equation | dynamic scaling

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 6/2018, Volume 228, Issue 3, pp. 995 - 1058

We construct a solution for the Complex Ginzburg–Landau equation in a critical case which blows up in finite time T only at one blow-up point...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | SEMILINEAR HEAT-EQUATIONS | SET | NO GRADIENT STRUCTURE | MULTI-BUMP | CONVECTION | STABILITY | BEHAVIOR | LIOUVILLE THEOREM | FLOW

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | SEMILINEAR HEAT-EQUATIONS | SET | NO GRADIENT STRUCTURE | MULTI-BUMP | CONVECTION | STABILITY | BEHAVIOR | LIOUVILLE THEOREM | FLOW

Journal Article

Annals of Physics, ISSN 0003-4916, 09/2018, Volume 396, pp. 397 - 428

.... Such equations can model phenomena described by complex Ginzburg–Landau systems under the added assumption of saturable media...

Cross-phase modulation | Modulational instability | Saturable nonlinearity | Complex Ginzburg–Landau system | Spatiotemporal dynamics | LINEAR SCHRODINGER-EQUATION | PHOTOREFRACTIVE CRYSTALS | PHYSICS, MULTIDISCIPLINARY | STABILITY | OPTICAL BEAMS | SPATIOTEMPORAL CHAOS | Complex Ginzburg-Landau system | INSTABILITIES | SOLITARY WAVES | LOCALIZED STRUCTURES | LIE SYMMETRIES | VECTOR-SOLITONS | Water waves | Numerical analysis | Segregation | Analysis | Physics - Pattern Formation and Solitons

Cross-phase modulation | Modulational instability | Saturable nonlinearity | Complex Ginzburg–Landau system | Spatiotemporal dynamics | LINEAR SCHRODINGER-EQUATION | PHOTOREFRACTIVE CRYSTALS | PHYSICS, MULTIDISCIPLINARY | STABILITY | OPTICAL BEAMS | SPATIOTEMPORAL CHAOS | Complex Ginzburg-Landau system | INSTABILITIES | SOLITARY WAVES | LOCALIZED STRUCTURES | LIE SYMMETRIES | VECTOR-SOLITONS | Water waves | Numerical analysis | Segregation | Analysis | Physics - Pattern Formation and Solitons

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 2/2017, Volume 350, Issue 1, pp. 105 - 128

We analyze 2-dimensional Ginzburg–Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | VORTEX MODULI SPACES | EQUATIONS | PHYSICS, MATHEMATICAL | CURVATURE

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | VORTEX MODULI SPACES | EQUATIONS | PHYSICS, MATHEMATICAL | CURVATURE

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 08/2018, Volume 32, Issue 24, p. 1850286

...–Landau equations are obtained using the auxiliary function method, Hirota method and the ansatz function technique under certain constraint conditions of coefficients in equations, respectively...

Hirota method | Ansatz function method | Auxiliary function method | 2D coupled complex Ginzburg-Landau equations | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | auxiliary function method | PHYSICS, MATHEMATICAL | ansatz function method

Hirota method | Ansatz function method | Auxiliary function method | 2D coupled complex Ginzburg-Landau equations | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | auxiliary function method | PHYSICS, MATHEMATICAL | ansatz function method

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 02/2020, Volume 131, p. 109471

•We study dynamics of dissipative solitons in a novel framework: complex Ginzburg-Landau equation of a fractional order...

Dissipative solitons | Fractional complex Ginzburg-Landau equation | Effective diffusion | GAP SOLITONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | BEAMS | SCHRODINGER-EQUATION | OPTICS | SPATIAL SOLITONS | PHYSICS, MATHEMATICAL

Dissipative solitons | Fractional complex Ginzburg-Landau equation | Effective diffusion | GAP SOLITONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | BEAMS | SCHRODINGER-EQUATION | OPTICS | SPATIAL SOLITONS | PHYSICS, MATHEMATICAL

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2018, Volume 61, pp. 248 - 270

....•A variety of structural changes in the moduli space of solutions of the complex Ginzburg–Landau equation were uncovered, in particular, in a subspace of group orbits of a very general class of invariant solutions not extensively studied...

Invariant solutions | Numerical continuation | Complex Ginzburg–Landau equation | Continuous symmetries | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | CHAOS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRY | Complex Ginzburg-Landau equation | DYNAMICS | CONVERGENCE | TIME-PERIODIC SOLUTIONS

Invariant solutions | Numerical continuation | Complex Ginzburg–Landau equation | Continuous symmetries | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | CHAOS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRY | Complex Ginzburg-Landau equation | DYNAMICS | CONVERGENCE | TIME-PERIODIC SOLUTIONS

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2019, Volume 45, pp. 877 - 894

In this paper, we are concerned with the local well-posedness of the initial–boundary value problem for complex Ginzburg–Landau (CGL...

Local well-posedness | Initial–boundary value problem | Subdifferential operator | Complex Ginzburg–Landau equation | MATHEMATICS, APPLIED | Initial-boundary value problem | Complex Ginzburg-Landau equation | FINITE-TIME BLOWUP

Local well-posedness | Initial–boundary value problem | Subdifferential operator | Complex Ginzburg–Landau equation | MATHEMATICS, APPLIED | Initial-boundary value problem | Complex Ginzburg-Landau equation | FINITE-TIME BLOWUP

Journal Article

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A new compact finite difference scheme for solving the complex Ginzburg–Landau equation

Applied Mathematics and Computation, ISSN 0096-3003, 06/2015, Volume 260, pp. 269 - 287

The complex Ginzburg–Landau equation is often encountered in physics and engineering applications, such as nonlinear transmission lines, solitons, and superconductivity...

Compact finite difference scheme | Complex Ginzburg–Landau equation | Stability | Ginzburg-Landau equation | Complex | MATHEMATICS, APPLIED | SUPERCONDUCTIVITY | Complex Ginzburg-Landau equation | APPROXIMATIONS | ELECTRICAL TRANSMISSION-LINE | SCHRODINGER-EQUATION | WISE ERROR ESTIMATE | TIME | MODEL | PULSES

Compact finite difference scheme | Complex Ginzburg–Landau equation | Stability | Ginzburg-Landau equation | Complex | MATHEMATICS, APPLIED | SUPERCONDUCTIVITY | Complex Ginzburg-Landau equation | APPROXIMATIONS | ELECTRICAL TRANSMISSION-LINE | SCHRODINGER-EQUATION | WISE ERROR ESTIMATE | TIME | MODEL | PULSES

Journal Article