Related papers: A domain wall between single-mode and bimodal stat…
In the Ginzburg-Landau equation, there are domain walls connecting two metastable states. The dynamics of domain walls has been intensively studied, but there remain still unsolved but crucial problems even for a single domain. We study the…
Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase equation, the interaction of such walls is…
We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schr{\"{o}}dinger equation, in which the modes are coupled by cross phase modulation (XPM). By means of continuation from various initial patterns taken in the…
Interactions of domain walls (DWs) are analyzed with relevance to formation of stationary bubbles (complexes of two DWs) and complexes of many domains in one dimensional systems. I investigate the domain structures in ferromagnets which are…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
The parametrically driven Ginsburg-Landau equation has well-known stationary solutions -- the so-called Bloch and Neel, or Ising, walls. In this paper, we construct an explicit stationary solution describing a bound state of two walls. We…
This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non-variational Slonczewski term for spin-torque effects.…
In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary…
Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states, in the form of domain walls (DWs) in the two-component…
We investigate 1D and 2D radial domain-wall (DW) states in the system of two nonlinear-Schr\"{o}dinger/Gross-Pitaevskii equations, which are coupled by the linear mixing and by the nonlinear XPM (cross-phase-modulation). The system has…
Interaction of domain walls (DWs) in ferromagnetic stripes is studied with relevance to the formation of stable complexes of many domains. Two DW system is described with the Landau-Lifshitz-Gilbert equation including regimes of narrow and…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
A powerful mathematical method for front instability analysis that was recently developed in the field of nonlinear dynamics is applied to the 1+1 (spatial and time) dimensional Landau-Lifshitz-Gilbert (LLG) equation. From the essential…
We work out domain walls in neutron $^{3}P_{2}$ superfluids realized in the core of neutron stars. Adopting the Ginzburg-Landau (GL) theory as a bosonic low-energy effective theory, we consider configurations of domain walls interpolating…
A condensed review is presented for two basic topics in the theory of pattern formation in nonlinear dissipative media: (i) domain walls (DWs, alias grain boundaries), which appear as transient layers between different states occupying…
We present a dynamical description and analysis of non-equilibrium transitions in the noisy one-dimensional Ginzburg-Landau equation for an extensive system based on a weak noise canonical phase space formulation of the Freidlin-Wentzel or…
We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. We derive an amplitude equation for the dynamics of the curvature close to the…
We consider a one-dimensional totally asymmetric exclusion process on a ring with extended inhomogeneities, consisting of several segments with different hopping rates. Depending upon the underlying inhomogeneity configurations and for…
The transition from phase chaos to defect chaos in the complex Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period P of MAWs is shown to be limited by a…
In this paper we describe domain walls appearing in a thin, nematic liquid crystal sample subject to an external field with intensity close to the Fr\'eedericksz transition threshold. Using the gradient theory of the phase transition…