相关论文: Normal Modes of the Small-Amplitude Oscillon
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the…
We study the minimizers of the sum of the principal Dirichlet eigenvalue of the negative Laplacian and the perimeter with respect to a general norm in the class of Jordan domains in the plane. This is equivalent (modulo scaling) to…
We consider static solutions of the sine-Gordon theory defined on a cylinder, which can be either periodic or quasi-periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential…
We study oscillons in D+1 space-time dimensions using a spherically symmetric ansatz. From Gaussian initial conditions, these evolve by emitting radiation, approaching ``quasi-breathers'', near-periodic solutions to the equations of motion.…
In this work, concentration properties of quasimodes for perturbed semiclassical harmonic oscillators are studied. The starting point of this research comes from the fact that, in the presence of resonances between frequencies of the…
We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify…
We use quantum sine-Gordon model to describe the low energy dynamics of a pair of coupled one-dimensional condensates of interacting atoms. We show that the nontrivial excitation spectrum of the quantum sine-Gordon model, which includes…
We study oscillons, extremely long-lived localized oscillations of a scalar field, with three different potentials: quartic, sine-Gordon model and in a new class of convex potentials. We use an absorbing boundary at the end of the lattice…
We study the magnetic properties of electron in a constant magnetic field and confined by a isotropic two dimensional harmonic oscillator on a space where the coordinates and momenta operators obey generalized commutation relations leading…
We consider an optically thin radiation-supported levitating atmosphere suspended well above the stellar surface, as discussed recently in the Schwarzschild metric for a star of luminosity close to the Eddington value. Assuming the…
Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition.…
We consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes - a nonlinear generalisation of the (symmetric and antisymmetric)…
We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave-functions of the two lowest-energy eigenstates for any momentum,…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy…
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…
In this work, we explore systematically various SO(2)-rotation-induced multiple dark-dark soliton breathing patterns obtained from stationary and spectrally stable multiple dark-bright and dark-dark waveforms in trapped one-dimensional,…
We describe the results of an experiment to test for spacetime anisotropy terms that might exist from Lorentz violations. The apparatus consists of a pair of cylindrical superconducting cavity-stabilized oscillators operating in the…
A scissors mode of a rotating Bose-Einstein condensate is investigated both theoretically and experimentally. The condensate is confined in an axi-symmetric harmonic trap, superimposed with a small rotating deformation. For angular…
The limit cycle of the van der Pol oscillator, $\ddot{x}+ \epsilon (x^2-1) \dot{x} + x =0$, is studied in the plane $(x,\dot{x})$ by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form…