Related papers: The emergence of a coherent structure for coherent…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate…
The paper continues a series of publications devoted to the 3D nonlinear localized coherent structures on the surface of vertically falling liquid films. The work is primarily focussed on experimental investigations. We study: (i)…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…
Recently, based on a supersymmetric approach, new classes of conditionally exactly solvable problems have been found, which exhibit a symmetry structure characterized by non-linear algebras. In this paper the associated ``non-linear''…
We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved…
Chimera states have attracted significant attention as symmetry-broken states exhibiting the unexpected coexistence of coherence and incoherence. Despite the valuable insights gained from analyzing specific systems, an understanding of the…
The original canonical coherent states could be defined in several ways. As applications for other sets of coherent states arose, the rules of definition were correspondingly changed. Among such rule changes were a change of group and…
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…
Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator"…
We study the stability of coherent structures in plane Couette flow against long-wavelength perturbations in wide domains that cover several pairs of coherent structures. For one and two pairs of vortices, the states retain the stability…
We discuss recent progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.
The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
We investigate the emergence of localized coherent behavior in a system consisting of two populations of social agents possessing a condition for non-interacting states, mutually coupled through global interaction fields. As an example of…
This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always…
The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or…
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…