Related papers: A method for bounding oscillatory integrals in ter…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
We consider preparation of nonclassical oscillatory states in a degenerate parametric oscillator combined with phase modulation. In this scheme intracavity oscillatory mode is excited by train of Gaussian laser pulses through degenerate…
A phase operator formulation for a recent model of interacting one-dimensional fermions in a harmonic trap is developed. The resulting theory is similar to the corresponding approach for the Luttinger model with open boundary conditions…
Oscillatory integral techniques are used to study the well-posedness of the KP-I equation for initial data that are small with respect to the norm of a weighted Sobolev space involving derivatives of total order no larger than 2.
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…
We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
In structural dynamics, energy dissipative mechanisms with non-viscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary…
We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed…
A recipe is presented for constructing band-limited superoscillating functions that exhibit arbitrarily high frequencies over arbitrarily long intervals.
We propose an explanation for the onset of oscillations seen in numerical simulations of dense, inclined flows of inelastic, frictional spheres. It is based on a phase transition between disordered and ordered collisional states that may be…