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On the invariants of the complex Ginzburg-Landau equation
Physics Letters A, 1984Abstract 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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A complex Ginzburg-Landau equation in magnetism
Journal of Magnetism and Magnetic Materials, 1995The 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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Lattice Boltzmann model for the complex Ginzburg-Landau equation
Physical Review E, 2010A 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, 1992A 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, 2009Pulse 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 +5 more
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X-wave solutions of complex Ginzburg-Landau equations
Physical Review E, 2006A 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, 2009The 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 +2 more
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Nonlocal Complex Ginzburg-Landau Equation for Electrochemical Systems
Physical Review Letters, 2008By 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 +1 more
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Recurrent motion in the fractional complex Ginzburg–Landau equation
Journal of Mathematical Physics, 2020This article concerns recurrent motion in the fractional complex Ginzburg–Landau equation with a small recurrent force. By using Galerkin’s method and energy estimate method, we obtain the existence of the bounded solutions, periodic solutions, quasiperiodic solutions, almost periodic solutions, and almost automorphic solutions under suitable ...
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Conservation laws of the complex Ginzburg-Landau equation
Physics Letters, Section A: General, Atomic and Solid State Physics, 2023Nikolai A Kudryashov
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