相关论文: Periodic magnetic curves in elliptic Sasakian spac…

In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…

This paper investigates curve flows on the light-cone in the 3-dimensional Minkowski space. We derive the Harnack inequality for the heat flow and present a detailed classification of space-periodic solitons for a third-order curvature…

The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of…

In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples:…

This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…

We study magnetic vortex-like solutions lying on the spherical surface. The simplest cylindrically symmetric vortex presents two cores (instead of one, like in open surfaces) with same charge, so repealing each other. However, the net…

This paper is concerned with the existence of pulsating travelling fronts for a KPP reaction-diffusion equation posed in a multi-dimensional periodic medium. We provide an alternative proof of the classic existence result. Our proof relies…

We obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle. These are (complete) constant scalar curvature metrics on the complement of $S^1$ inside $S^m$, $m\geq 5$,…

We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…

There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…

We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…

The motion of compressible, inviscid fluid under the constant pressure on a rotating sphere is studied. The hodograph equations for the corresponding Euler equation are presented. They provide us with the class of solutions of the Euler…

We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…

We prove that all elliptic curves defined over real quadratic fields are modular.

The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…

Comet-type periodic orbits of the circular restricted three-body problem (CR3BP) are periodic solutions that are generated from very large retrograde and direct circular Keplerian motions around the common center of mass of the primaries.…

Periodic measures are the time-periodic counterpart to invariant measures for dynamical systems and can be used to characterise the long-term periodic behaviour of stochastic systems. This paper gives sufficient conditions for the…

We show that S. Saito's fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a…

The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed…

The paper studies existence of solutions for the nonlinear Schr\"odinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is…