Related papers: Phase-Diffusion Equations for the Anisotropic Comp…
Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the…
We study the dynamics of holes and defects in the 1D complex Ginzburg--Landau equation in ordered and chaotic cases. Ordered hole--defect dynamics occurs when an unstable hole invades a plane wave state and periodically nucleates defects…
We study the spatiotemporally chaotic dynamics of holes and defects in the 1D complex Ginzburg--Landau equation (CGLE). We focus particularly on the self--disordering dynamics of holes and on the variation in defect profiles. By enforcing…
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The…
The A and B phases of superfluid 3 He have vector degrees of freedom that reflect their characteristic broken symmetries, respectively chiral and spin-orbit rotation axes. Anisotropic disorder in the superfluid, imbibed in uniformly…
This work studies the effects of a through-flow on two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid confined between two plane plates, as a model problem to further our understanding of the fluid mechanics in the…
The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is shown that a straight vortex line is unstable with respect to spontaneous…
We study the nature of the instability of the homogeneous steady states of the subcritical Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by…
We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear…
Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
The maximal conserved phase gradient is introduced as an order parameter to characterize the transition from phase- to defect-turbulence in the complex Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime and…
The response of spiral waves to external perturbations in a stable regime of the two-dimensional complex Ginzburg-Landau equation (CGLE) is investigated. It is shown that the spiral core has a finite mobility and performs Brownian motion…
In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction-diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the…
Spatial non-homogeneities can synchronize clusters of spatially-extended oscillators in different frequency plateaus. Motivated by physiological rhythms, we fully characterize the phase diagram of a Ginzburg-Landau (GL) model with a…
We consider the Ginzburg-Landau equation, $ \partial_t u= \partial_x^2 u + u - u|u|^2 $, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it…
We consider a model proposed earlier by us for describing a form of plastic instability found in creep experiments . The model consists of three types of dislocations and some transformations between them. The model is known to reproduce a…
A model for homogeneous anisotropic incompressible turbulence is proposed. The model generalizes the GISS model of homogeneous isotropic turbulence; the generalization involves the solution of the GISS equations along a set of integration…
We study the disordered, multi-spiral solutions of two-dimensional homogeneous oscillatory media for parameter values at which the single spiral/vortex solution is fully stable. In the framework of the complex Ginzburg-Landau (CGLE)…
We extend the results of previous work on the vortex order parameter in systems similar to the Ginzburg-Landau description of superfluid $^3$He in the bulk B phase. Specifically, we consider vortices preserving an axial $U(1)$ symmetry. We…