منابع مشابه
The Complex Ginzburg-landau Equation∗
Essential to the derivation of the Ginzburg-Landau equation is assumption that the spatial variables of the vector field U(x, y, t) are defined on a cylindrical domain. This means that (x, y) ∈ R ×Ω, where Ω ⊂ R is a open and bounded domain (and m ≥ 1, n ≥ 0), so that U : R ×Ω×R+ → R . The N ×N constant coefficient matrix Sμ is assumed to be non-negative, in the sense that all its eigenvalues a...
متن کاملThe Ginzburg–Landau equation III. Vortex dynamics
In this paper we study the time-dependent Ginzburg–Landau equation of the Schrödinger type in two dimensions. The initial conditions are chosen to describe several well-separated vortices. Our task is to understand the vortex structure of the corresponding solutions as well as corrections due to radiation. To this end we develop the nonlinear adiabatic theory. Using the methods of effective act...
متن کاملPeriodic Solutions of the Ginzburg-landau Equation
Spatially periodic solutions to the Ginzburg-Landau equation are considered. In particular we obtain: criteria for primary and secondary bifurcation; limit cycle solutions; nonlinear dispersion relations relating spatial and temporal frequencies. Only relatively simple tools appear in the treatment and as a result a wide range of parameter cases are considered. Finally we briefly treat the case...
متن کاملDynamic Bifurcation of the Ginzburg-Landau Equation
We study in this article the bifurcation and stability of the solutions of the Ginzburg–Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as λ crosses the first critical value of the linear problem. Bifurcations from the rest of the eigenvalues of the linear problem are ...
متن کاملDiffusive repair for the Ginzburg-Landau equation
We consider the Ginzburg-Landau equation for a complex scalar field in one dimension and show that small phase and amplitude perturbations of a stationary solution repair diffusively to converge to a stationary solution. Our methods explain the range of validity of the phase equation, and the coupling between the “fast” amplitude equation and the “slow” phase equation.
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1995
ISSN: 0898-1221
DOI: 10.1016/0898-1221(94)00222-7