Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex media
From MaRDI portal
Publication:2478737
DOI10.1016/j.physleta.2005.01.047zbMath1135.82320arXivcond-mat/0309577OpenAlexW2002285260MaRDI QIDQ2478737
Alexander V. Milovanov, Jens Juul Rasmussen
Publication date: 25 March 2008
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/cond-mat/0309577
Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Dynamic critical phenomena in statistical mechanics (82C27)
Related Items (44)
Galerkin finite element method for the nonlinear fractional Ginzburg-Landau equation ⋮ Soliton dynamics in a fractional complex Ginzburg-Landau model ⋮ Map of discrete system into continuous ⋮ Black swans, extreme risks, and the e-pile model of self-organized criticality ⋮ A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations ⋮ Coupled oscillators with power-law interaction and their fractional dynamics analogues ⋮ The inviscid limit of the fractional complex Ginzburg-Landau equation ⋮ High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations ⋮ Well-posedness of space fractional Ginzburg-Landau equations involving the fractional Laplacian arising in a Bose-Einstein condensation and its kernel based approximation ⋮ Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation ⋮ High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation ⋮ Exponential Runge-Kutta method for two-dimensional nonlinear fractional complex Ginzburg-Landau equations ⋮ Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative ⋮ Monotonicity and one-dimensional symmetry of solutions for fractional reaction-diffusion equations and various applications of sliding methods ⋮ Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation ⋮ Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations ⋮ High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation ⋮ Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation ⋮ A Liouville theorem for the fractional Ginzburg-Landau equation ⋮ Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain ⋮ Fractional dynamics of coupled oscillators with long-range interaction ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The solution of fractional nonlinear Ginzburg-Landau equation with weak initial data ⋮ An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equations ⋮ Fractional generalization of Kac integral ⋮ A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation ⋮ An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation ⋮ On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres ⋮ Universality of non-extensive Tsallis statistics and time series analysis: theory and applications ⋮ An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation ⋮ Fractional dynamics of systems with long-range interaction ⋮ A linearized Crank–Nicolson Galerkin FEMs for the nonlinear fractional Ginzburg–Landau equation ⋮ Well-posedness of the fractional Ginzburg–Landau equation ⋮ An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation ⋮ On fractional and fractal formulations of gradient linear and nonlinear elasticity ⋮ High-dimensional nonlinear Ginzburg-Landau equation with fractional Laplacian: discretization and simulations ⋮ An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian ⋮ Non-linear fractional field equations: weak non-linearity at power-law non-locality ⋮ Well-posedness of fractional Ginzburg–Landau equation in Sobolev spaces ⋮ Asymptotic estimates for an integral equation in theory of phase transition ⋮ Fractional Schrödinger equation in gravitational optics ⋮ A NOVEL VARIATIONAL APPROACH FOR FRACTAL GINZBURG–LANDAU EQUATION ⋮ A fourth-order linearized difference scheme for the coupled space fractional Ginzburg-Landau equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Introduction to multifractals in dynamical systems theory and fully developed fluid turbulence
- Fractional kinetic equation for Hamiltonian chaos
- Fractal random walks
- Some applications of fractional equations.
- Numerical simulation of anomalous plasma transport in the presence of magnetic turbulence.
- Evidence of fractional transport in point vortex flow
- Chaos, fractional kinetics, and anomalous transport
- Self-organized criticality
- Fractional kinetic equations: solutions and applications
- Theory of Superconductivity
This page was built for publication: Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex media
