Waves in the Skyrme--Faddeev model and integrable reductions

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation of periodic wave states, leading to a quasi-linear system. The reduction to general hydrodynamic systems have been considered and it is compared with other integrable reductions of the system.Comment: 16 pages, 5 figure

Polarization of Thermal X-rays from Isolated Neutron Stars

Since the opacity of a magnetized plasma depends on polarization of radiation, the radiation emergent from atmospheres of neutron stars with strong magnetic fields is expected to be strongly polarized. The degree of linear polarization, typically ~10-30%, depends on photon energy, effective temperature and magnetic field. The spectrum of polarization is more sensitive to the magnetic field than the spectrum of intensity. Both the degree of polarization and the position angle vary with the neutron star rotation period so that the shape of polarization pulse profiles depends on the orientation of the rotational and magnetic axes. Moreover, as the polarization is substantially modified by the general relativistic effects, observations of polarization of X-ray radiation from isolated neutron stars provide a new method for evaluating the mass-to-radius ratio of these objects, which is particularly important for elucidating the properties of the superdense matter in the neutron star interiors.Comment: 7 figures, to be published in Ap

Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models

New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics behaviour are presented as an example. The special attention is paid for the singular case $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur

Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio