Related papers: Periodic Vortex Streets and Complex Monodromy
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schr\"odinger equation on two-dimensional flat tori. This is achieved by performing a second microlocalization related to the size of the…
A numerical scheme to study the mixed states in a mesoscopic type-II superconducting cylinder is described. Steady-state configurations and transient behavior of the magnetic vortices for various values of the applied magnetic field H are…
A non-relativistic scalar field coupled minimally to electromagnetism supports in the presence of a homogeneous background electric charge density the existence of smooth, finite-energy topologically stable flux vortices. The static…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…
We count invertible Schr\"odinger operators (perturbations by diagonal matrices of the adjacency matrix) over finite fieldsfor trees, cycles and complete graphs.This is achieved for trees through the definition and use of local invariants…
We give a class of explicit solutions for the stationary and cylindrically symmetric vortex configurations for a ``cool'' two-component superfluid (i.e. superfluid with an ideal gas of phonons). Each solution is characterized only by a set…
We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schr\"odingers operator associated with the alloy type potential restricted to finite volume subgraphs…
In this paper we showed an equivalence of notions of regularity, transitivity and Ergodic principle for quadratic stochastic Volterra operators acting on the finite dimensional simplex.
A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting…
This work is devoted to the study of a family of almost periodic one-dimensional Schr\"odinger equations. We define a monodromy matrix for this family. We study the asymptotic behavior of this matrix in the adiabatic case. Therefore, w…
We analyze existence, stability, and symmetry of point vortex relative equilibria with one dominant vortex and N vortices with infinitesimal circulation. The dimension of the problem can be reduced by taking an infinitesimal circulation…
In this paper we constructively determine a family of the spectral invariants of the multidimensional Schrodinger operator with a periodic potential by the given band functions.
We consider the classical dynamics of a particle in a $d=2,3$-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify…
We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases…
We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.
We establish an existence theorem for the doubly periodic vortices in a generalized self-dual Chern--Simons model. We show that there exists a critical value of the coupling parameter such that there exits self-dual doubly periodic vortex…
The two-dimensional laminar vortex streets behind a triangle have two morphologically distinct structures depending on the Reynolds number and the aspect ratio of the triangle. These two structures are the conventional structure and the…
By means of variational methods, in this paper, we establish sharp existence results for solutions of the master equations governing `fractional multiple vortices.' In the doubly periodic situation, the conditions for existence are both…
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…