Related papers: The capture into parametric autoresonance
In [5] the structure of the bifurcation diagrams of a class of superlinear indefinite problems with a symmetric weight was ascertained, showing that they consist of a primary branch and secondary loops bifurcating from it. In [4] it has…
The Brownian dynamics of an optically trapped water droplet are investigated across the transition from over to under-damped oscillations. The spectrum of position fluctuations evolves from a Lorentzian shape typical of over-damped systems…
In this paper, the high-frequency diffraction of a plane wave incident along a planar boundary turning into a smooth convex contour, so that the curvature undergoes a jump, is asymptotically analysed. An approach modifying the Fock…
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\'es, L.M.…
We investigate the bifurcation structure of the Kuramoto-Sivashinsky equation with homogeneous Dirichlet boundary conditions. Using hidden symmetry principles, based on an extended problem with periodic boundary conditions and $\Otwo$…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
Two-frequency radiative transfer (2f-RT) theory is developed for classical waves in random media. Depending on the ratio of the wavelength to the scale of medium fluctuation 2f-RT equation is either a Boltzmann-like integral equation with a…
Two-point super-resolution is an important problem in many signal processing applications. In this paper, we aim to establish a resolution theory for two-point super-resolution from a single snapshot. We consider a complex two-point model…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite…
We present a theoretical analysis of two-photon absorption of classical and squeezed light valid when one-photon absorption to an intermediate state is either resonant or far-detuned from resonance, and in both the low and high intensity…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…
Based on a comparison principle, we derive an exponential rate of convergence for solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in one space dimension. We then apply the result to some models…
Here we analyze ways to achieve deep subthreshold parametric squeezing or cooling of a single degree-of-freedom parametric resonator enhanced by a lock-in amplifier feedback loop. Due to the feedback, the dynamics of the parametric…
Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state…
In this paper, we find all possible asymptotic behaviours of the solutions of the second Painlev\'e equation $y''=2y^3+xy +\alpha$ as the parameter $\alpha\to\infty$ in the local region $x\ll\alpha^{2/3}$. We prove that these are asymptotic…
This paper illustrates the application of Lie transform normal-form theory to the construction of the 1:2 resonant normal form corresponding to a wide class of natural Hamiltonian systems. We show how to compute the bifurcations of the main…
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near a given algebraic plane curve. Our solutions are complex contour integral…
This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the obstacle is trapping. There are two resolvent estimates for…