We develop a Landau-Ginzburg theory of the hidden-order phase and the local moment antiferromagnetic phase of URu2Si2. We unify the two broken symmetries in a common complex-order parameter and derive many experimentally relevant consequences such as the topology of the phase diagram in magnetic field and pressure. The theory accounts for the appearance of a moment under application of stress a...

A method is presented which results in low-dimensional dynamical systems for situations in which low-dimensional attractors are known to exist. The method is based on the use of the Karhunen-Loeve procedure for the determination of an optimal basis and the subsequent use of the Galerkin procedure to generate the dynamical system. The method is applied to two problems for the Ginzburg-Landau equ...

We introduce a spatially localized inhomogeneity into the two-dimensional complex Ginzburg-Landau equation. We observe that this can produce two types of target wave patterns: stationary and breathing. In both cases, far from the target center, the field variables correspond to an outward propagating periodic traveling wave. In the breathing case, however, the region in the vicinity of the targ...

We study in this paper the bifurcation and stability of the solutions of the complex Ginzburg–Landau equation(CGLE). We investigate two different modes of CGLE. We study the first mode of CGLE which has only cubic unstable nonlinear term and later we also study the second mode of CGLE which has both cubic and quintic nonlinear terms. The solutions considered in cubic CGLE bifurcate from the tri...

We study the dynamics of the one-dimensional complex Ginzburg Landau equation (CGLE) in the regime where holes and defects organize themselves into composite superstructures which we call zigzags. Extensive numerical simulations of the CGLE reveal a wide range of dynamical zigzag behavior which we summarize in a “phase diagram”. We have performed a numerical linear stability and bifurcation ana...