A method for analysis of essentially nonlinear vibrations of cyclically symmetric structure has been developed. Two major cases are analysed: (i) steady-state periodic multiharmonic vibrations; (ii) transient vibrations. The method allows exact calculation of the essentially nonlinear vibrations to be performed using a model for only one period of the cyclic symmetry. A rigorously proof of poss...

Numerical solutions of the Einstein-Yang-Mills equations with a negative cosmological constant are constructed. These axially symmetric solutions approach asymptotically the anti-de Sitter spacetime and are regular everywhere. They are characterized by the winding number n > 1, the mass and the non-Abelian magnetic charge. The main properties of the solutions and the differences with respect to...

The joint interactions of hydrodynamics, radiative transfer and photochemistry destabilize a hydrodynamic system that would otherwise stable. This observation is of important interest in itself. In this paper, the stability of baroclinic, axially symmetric vortex on an f-plane to axially symmetric disturbances is studied. It is found that with photochemistry and radiative transfer disturbances ...

A theory of parametric amplification in a filamentary electron beam by transverse fields is developed in coupled mode form. Space charge effects are neglected. In addition to beam modes at the signal frequency, beam modes at frequencies wn=w+wv, n=O, ±1, ±2· ··,where wp is the pump frequency, are coupled together. A discussion of the general form of the equations is given and reveals the circum...

It is well-known that the Einstein-Maxwell equations reduce in the stationary and axially symmetric case to an axially symmetric harmonic map with prescribed singularities ': R 3 n ! H 2 C , where is a subset of the axis of symmetry, and H 2 C is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities ': R n n...

It is well-known that the Einstein-Maxwell equations reduce in the stationary and axially symmetric case to an axially symmetric harmonic map with prescribed singularities ': R 3 n ! H 2 C , where is a subset of the axis of symmetry, and H 2 C is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities ': R n n...