Related papers: Periodic Vortex Streets and Complex Monodromy
We construct the solution to the periodic Cauchy problem of the Schr\"odinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric algorithm of solving this periodic Cauchy problem follows.…
We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase…
This paper aims to provide a robust model for the well-known phenomenon of K\'arm\'an Vortex Street arising in Fluid Mechanics. The first theoretical attempt to model this pattern was given by von K\'arm\'an [22, 23]. He considered two…
We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions.…
The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with…
The nonlinear Ginzburg-Landau equations are solved numerically in order to investigate the vortex structure in thin superconducting disks of arbitrary shape. Depending on the size of the system and the strength of the applied magnetic field…
We develop precise analytic description of oscillons - long-lived quasiperiodic field lumps - in scalar field theories with nearly quadratic potentials, e.g. the monodromy potential. Such oscillons are essentially nonperturbative due to…
We consider a two-component, two-dimensional nonlinear Schr\"{o}dinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a…
We study discrete vortices in coupled discrete nonlinear Schrodinger equations. We focus on the vortex cross configuration that has been experimentally observed in photorefractive crystals. Stability of the single-component vortex cross in…
Three types of streamline topology in a Karman vortex street flow are shown under the variation of spatial parameters. For the motion of dilute particles in the K\'arm\'an vortex street flow, there exist a route of bifurcation to a chaotic…
We revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable…
A periodic Schr\"odinger operator on a noncompact Riemannian manifold $M$ such that $H^1(M, \mathbb R)=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group is considered. Under some additional conditions…
The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter…
The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a…
We study positivity, localization of binding and essential self-adjointness properties of a class of Schroedinger operators with many anisotropic inverse square singularities, including the case of multiple dipole potentials.
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
The vortex patterns stabilized by the square array of artificial pinning sites with a tunable pinning strength are studied by using a phenomenological approach in the London limit. The transitions between pinned and deformed triangular…