Showing papers in "Physica D: Nonlinear Phenomena in 2018"

TL;DR: In this paper, the authors study the global well-posedness and stability/instability of perturbations near a special type of hydrostatic equilibrium associated with the 2D Boussinesq equations without buoyancy.

TL;DR: In this article, the concept of Lagrangian Coherent Structure (LCS) is generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid.

TL;DR: In this paper, the inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrodinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interaction and ferromagnetic spins exchange interactions(self-focusing case).

TL;DR: In this article, the authors show that wave breaking occurs with positive probability for the stochastic Camassa-Holm (SCH) equation with a positive probability, and conjecture that the time-asymptotic solutions of the SCH will consist of emergent wave trains of peakons moving along time paths.

TL;DR: In this article, the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal, was examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results.

TL;DR: In this article, the authors examined the scattering processes among the members of a rich family of kinks which arise in a (1+1)-dimensional relativistic two scalar field theory.

TL;DR: In this paper, the Ablowitz-Ladik system is used to demonstrate how to analyze initial boundary value problems for integrable nonlinear differential difference equations via the unified transform (Fokas method).

TL;DR: In this article, the authors established backward compactness of a pullback random attractor (PRA) from a backward limit-set compact cocycle, which is a necessary and sufficient condition such that its time-fibers are upper semi-continuous at negative infinity.

TL;DR: In this paper, the authors prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of R 2 when fractional Dirichlet Laplacian dissipation is added.

TL;DR: In this article, the authors consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour.

TL;DR: This paper shows that certain noise diffusion processes can drive an unsynchronized network towards synchronization, and explicitly shows that a sufficiently large noise can drive a population towards a common decision.

TL;DR: In this paper, it was shown that the upper semi-continuity of the pullback attractor of a non-autonomous random dynamical system has an equivalence relationship with the uniform compactness of the local union ∪ s ∈ I A s ( ω ), where I ⊂ R is compact.

TL;DR: This work introduces and study a model which takes into account two different attachment rules: a preferential attachment mechanism that stresses the rich get richer system and a uniform choice for the most recent nodes, i.e. the nodes belonging to a window of size w to the left of the last born node.

TL;DR: In this paper, the existence and uniqueness of 2D Boussinesq equations with partial dissipation in bounded domains with the Navier type boundary conditions were proved under minimal regularity assumptions on the initial data.

TL;DR: In this article, a determining wavenumber for the surface quasi-geostrophic (SQG) equation defined for each individual trajectory was introduced and its dependence on the force was studied.

TL;DR: In this paper, the Ordered Line Integral Method (OLIM) is extended for computing the quasi-potential for 2D SDEs with anisotropic and position-dependent diffusion scaled by a small parameter on a regular rectangular mesh.

TL;DR: In this article, the interaction between two non-radially symmetric camphor particles is theoretically investigated and the equation describing the motion is derived as an ordinary differential system for the locations and the rotations.

TL;DR: In this paper, the authors used the Chapman-Enskog expansion to derive hydrodynamic approximations of the Bose-Einstein condensate and excited atoms.

TL;DR: In this article, a general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases, and the evolution equation for the multimode characteristic function Z is obtained within an interaction representation and a perturbation expansion in the small nonlinearity parameter.

TL;DR: In this paper, the authors studied the effect of a spatially variable bulk feed term in the reaction kinetics of two-component reaction-diffusion (RD) systems in the singular limit of a large diffusivity ratio.

TL;DR: In this paper, the authors describe differences between synchronisation and resonance, and analyse different types of nonlinear resonances in a weakly damped Duffing oscillator using bifurcation theory techniques.

TL;DR: In this paper, the authors define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifold of L 1, L 2.

TL;DR: In this paper, the authors present a solution to the Navier-Stokes equations driven by a random force, where the first emergence of anomalous scaling is observed out of a low-R e Gaussian background.

TL;DR: In this article, a spectral measure of order based on the Fourier transform, a geometric measure using the Delaunay triangulation, and topological measures of order were compared for nearly hexagonal, planar lattices.

TL;DR: In this article, a numerical approach based on string method is proposed to identify local maximum likelihood paths (MLPs) associated with each attractor on the separatrix, such as saddle point or hyperbolic periodic orbit.

TL;DR: In this paper, the authors studied the existence of entire solutions of the Allen-Cahn equation in one-dimensional Euclidean space and showed that there are no entire solutions originating from more than four fronts.

TL;DR: In this article, a multiple time scales analysis for the Swift-Hohenberg equation with delayed feedback via Pyragas control, with and without additive noise, is provided, where the delay can drive the appearance of an additional time scale, intermediate to the usual slow and fast time scales observed in the modulation of rolls without delay.

TL;DR: In this paper, the authors investigated certain phenomena associated with the dynamics of pulse solutions for a FitzHugh-Nagumo reactiondiffusion model and demonstrated that the pulses will move so as to maximize the strength of activation or minimize that of inhibition.

TL;DR: In this paper, the synchronization of chaotic systems when the coupling between them contains both time averages and stochastic noise is studied and it is shown that in the presence of noise the convergence is to within a factor of the variance of the noise.

TL;DR: In this article, it was shown that spherically symmetric perturbations of stable polytropic steady states of the Vlasov-Poisson system lead to solutions which oscillate in time.