Related papers: Nonlinear resonances in the $ABC$-flow
In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the…
There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…
In this paper it is proved that near a compact, invariant, proper subset of a continuous flow on a compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. This result shows…
We discuss the resonances of Hamiltonians with constant electric field in one dimension in the limit of small field. These resonances occur near the real axis, near zeros of the analytic continuation of a reflection coefficient for…
Motion of a cylinder dynamically interacting with n point vortices in a perfect fluid is considered. A nonliniear Poisson structure and two integrals of motion are found. The equations of motion a priori are not Hamiltonian. For n=1, the…
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
We consider stability of steady convective flows in a horizontal layer with stress-free boundaries, heated below and rotating about the vertical axis, in the Boussinesq approximation (the Rayleigh-Benard convection). The flows under…
Convection in a cylindrical container of small aspect ratio is studied. It is known that when, in addition to buoyancy forces, thermocapillarity effects are taken into account, resonant interactions of two modes may appear. In the case of…
Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [V. M. Malkin and N. J. Fisch, Physical Review E 108, 045208 (2023)]. The high order resonance is a unique…
In this paper we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the interplay between baroclinic and barotropic dynamics in a…
We explore the harmonic-Ricci flow---that is, Ricci flow coupled with harmonic map flow---both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate…
Persistent currents in disordered mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalization methods in the one-dimensional (1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D) systems.…
In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…
In this work, two multi-harmonic Hamiltonian models for mean motion resonances are formulated and their applications to first-order resonances are discussed. For the $k_p$:$k$ resonance, the usual critical argument $\varphi = k \lambda -…
We study the cubic wave equation in AdS_(d+1) (and a closely related cubic wave equation on S^3) in a weakly nonlinear regime. Via time-averaging, these systems are accurately described by simplified infinite-dimensional quartic Hamiltonian…
A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the…
We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic…