Results 191 to 200 of about 2,507 (215)

Potential for the Complex Ginzburg-Landau Equation

Europhysics Letters (EPL), 1990
A generalized thermodynamic potential is derived for spatially extended pattern-forming nonequilibrium systems whose order parameter obeys the complex Ginzburg-Landau equation in one spatial dimension. The real potential, generalizing the Ginzburg-Landau free energy, is shown to describe typical nonequilibrium phenomena like the Newell-Kuramoto and the
R Graham, T Tél
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The complex Ginzburg–Landau equation: an introduction

Contemporary Physics, 2012
The complex Ginzburg–Landau equation (CGLE), probably the most celebrated nonlinear equation in physics, describes generically the dynamics of oscillating, spatially extended systems close to the onset of oscillations. Using symmetry arguments, this article gives an easy access to this equation and an introduction into the rich spatio-temporal ...
Vladimir García-Morales, Katharina Krischer   +1 more
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On the invariants of the complex Ginzburg-Landau equation

Physics Letters A, 1984
Abstract Using Lie group theory, both the invariants and the similarity variables of the complex Ginzburg—Landau equation Vxx = a(Vt + bV) + cV|V|2kwherea,b,cϵIandkϵI are constructed.
Michael Magen, Philip Rosenau
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Lattice Boltzmann model for the complex Ginzburg-Landau equation

Physical Review E, 2010
A lattice Boltzmann model with complex distribution function for the complex Ginzburg-Landau equation (CGLE) is proposed. By using multiscale technique and the Chapman-Enskog expansion on complex variables, we obtain a series of complex partial differential equations. Then, complex equilibrium distribution function and its complex moments are obtained.
Jianying, Zhang, Guangwu, Yan
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Dynamics of the globally coupled complex Ginzburg-Landau equation

Physical Review A, 1992
A discrete version of the complex Ginzburg-Landau equation is studied on a completely connected lattice of N sites. This can equivalently be described as a model of N identical globally coupled limit-cycle oscillators. The phase diagram is obtained by a combination of numerical and analytical techniques.
, Hakim, , Rappel
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Dissipative Solitons in Coupled Complex Ginzburg–Landau Equations

Journal of the Physical Society of Japan, 2009
Pulse propagation in inhomogeneous nonlinear media with linear and nonlinear gain and loss, described by a system of nonlinearly coupled complex Ginzburg–Landau equations (CGLEs) with variable coefficients, is considered. Exact solitary pulse (SP) solutions are obtained analytically, for special choices of variable coefficients of the nonlinear gain ...
Malomed, B, Pak, OS, Lam, CK, Nakkeeran, K, Senthilnathan, K, Chow, KW   +5 more
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A complex Ginzburg-Landau equation in magnetism

Journal of Magnetism and Magnetic Materials, 1995
The complex Ginzburg-Landau equation corresponding to subcritical bifurcation is derived from a Landau-Lifshitz-Gilbert equation of motion of the magnetization in a one-dimensional uniaxial ferromagnet. The validity of this approximation is tested by a numerical simulation.
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X-wave solutions of complex Ginzburg-Landau equations

Physical Review E, 2006
A solution in the form of X-wave patterns of the complex Ginzburg-Landau equation with a harmonic background inhomogeneity is obtained. The pattern can be attributed to the effects of the harmonic potential and the boundary configuration and size. By varying the harmonic of the background potential, the competition among three types of wave patterns ...
C T, Zhou, M Y, Yu, X T, He
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Quasiperiodic solutions for the cubic complex Ginzburg–Landau equation

Journal of Mathematical Physics, 2009
The existence of two-dimensional Kolmogorov–Arnold–Moser invariant tori is proved for cubic complex Ginzburg–Landau equation of higher spatial dimension. As a consequence, the equation possesses a Cantorian branch of nontraveling-wave quasiperiodic solutions of two-dimensional frequency vector.
Cong, Hongzi, Liu, Jianjun, Yuan, Xiaoping   +2 more
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Nonlocal Complex Ginzburg-Landau Equation for Electrochemical Systems

Physical Review Letters, 2008
By means of an extended center-manifold reduction, we derive the nonlocal complex Ginzburg-Landau equation (NCGLE) valid for electrochemical systems with migration coupling. We carry out the stability analysis of the uniform oscillation, elucidating the role of the nonlocal coupling in electrochemical systems at the vicinity of a supercritical Hopf ...
Vladimir, García-Morales, Katharina, Krischer   +1 more
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