The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.Comment: 11 pages, 1 figur

Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics

A class of integrable 2-dim classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With similar technique a new class of potentials connected with Lax method is found which provides the integrability of corresponding 2-dim hamiltonian systems. In addition, some integrable 2-dim systems with potentials expressed in elliptic functions are explored.Comment: 19 pages, LaTeX, final version to be published in J.Phys.

Chaotic Phenomenon in Nonlinear Gyrotropic Medium

Nonlinear gyrotropic medium is a medium, whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself a model of nonlinear coupled oscillators. This article is devoted to the study of the Kuhn's nonlinear model. In the first paragraph of the paper we study classical dynamics in case of weak as well as strong nonlinearity. In case of week nonlinearity we have obtained the analytical solutions, which are in good agreement with the numerical solutions. In case of strong nonlinearity we have determined the values of those parameters for which chaos is formed in the system under study. The second paragraph of the paper refers to the question of the Kuhn's model integrability. It is shown, that at the certain values of the interaction potential this model is exactly integrable and under certain conditions it is reduced to so-called universal Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical consideration. It shows the possibility of stochastic absorption of external field energy by nonlinear gyrotropic medium. The last forth paragraph of the paper is devoted to generalization of the Kuhn's model for infinite chain of interacting oscillators

Symplectic Structures for the Cubic Schrodinger equation in the periodic and scattering case

We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schr\"{o}dinger equation.Comment: This is expanded and corrected versio

Spectroscopy with random and displaced random ensembles

Due to the time reversal invariance of the angular momentum operator J^2, the average energies and variances at fixed J for random two-body Hamiltonians exhibit odd-even-J staggering, that may be especially strong for J=0. It is shown that upon ensemble averaging over random runs, this behaviour is reflected in the yrast states. Displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced BE2 transitions for a certain class of model spaces. It is explained how to generalize these results to other forms of collectivity.Comment: 4 pages, 4 figure

The Lake Baikal neutrino experiment: selected results

We review the present status of the lake Baikal Neutrino Experiment and present selected physical results gained with the consequetive stages of the stepwise increasing detector: from NT-36 to NT-96. Results cover atmospheric muons, neutrino events, very high energy neutrinos, search for neutrino events from WIMP annihilation, search for magnetic monopoles and environmental studies. We also describe an air Cherenkov array developed for the study of angular resolution of NT-200.Comment: 25 pages, 12 figures. To appear in the Procrrdings of International Conference on Non-Accelerator New Physics, June 28 - July 3, 1999, Dubna, Russi

BAIKAL experiment: status report

We review the present status of the Baikal Neutrino Project and present the results obtained with the deep underwater neutrino telescope NT-200.Comment: 4 pages, 3 figures. Presented at TAUP 2001 (7th international workshop on Topics in Astroparticle and Underground Physics), Sep. 2001, Laboratori Nazionali del Gran Sasso, Assergi, Ital