Related papers: Countable periodic solutions of the Lorentz force …

In this paper, by means of the Melnikov functions we consider bifurcations of harmonic or subharmonic solutions from a periodic solution of a planar Hamiltonian system under impulsive perturbation. We give some sufficient conditions under…

We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…

As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

Periodic travelling waves are considered in the class of reduced Ostrovsky equations that describe low-frequency internal waves in the presence of rotation. The reduced Ostrovsky equations with either quadratic or cubic nonlinearities can…

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In…

We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the…

In this note, we present a new proof of the solvability of the electrostatic Born-Infeld equation with radial charge, based on the conformal method and the Spacetime Positive Energy Theorem. An advantage of this approach is that the…

We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schr\"odinger equation…

Existence of non-resonant solutions of time-periodic type are established for the Kuznetsov equation with a periodic forcing term. The equation is considered in a three-dimensional whole-space, half-space and bounded domain, and with both…

In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…

We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results extend to cases where a possibly singular scalar potential is…

We study periodic solutions for a quasi-linear system, which is the so called dispersionless Lax reduction of the Benney moments chain. This question naturally arises in search of integrable Hamiltonian systems of the form $ H=p^2/2+u(q,t)…

In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of…

One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg…

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a…

We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…

Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…

For $n$-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the…