Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal

The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while shorter wavelengths may be unstable. The possibility for the formation and propagation of different envelope localized excitations is discussed. It is shown that the total grain displacement bears a (weak) constant displacement (zeroth harmonic mode), due to the asymmetric form of the nonlinear interaction potential. The existence of asymmetric envelope localized modes is predicted. The types and characteristics of these coherent nonlinear structures are discussed.Comment: 18 pages, 7 figures, to appear in Physics of Plasma

Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.Comment: 12 page

Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions

In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions. This method is based on a homogeneous integral equation with a nontrivial kernel, which allows one to reduce the nonlinear PDEs to systems of non-differential (algebraic or transcendental) equations for the unknown fields. In the simplest examples, the above dressing scheme captures matrix equations integrated by the characteristics method and nonlinear PDEs associated with matrix Hopf-Cole transformations.Comment: 31 page

Collinear Photon Emission from the Quark-Gluon Plasma: The Light-Cone Path Integral Formulation

We give a simple physical derivation of the photon emission rate from the weakly coupled quark-gluon plasma connected with the collinear processes $q\to \gamma q$ and $q\bar{q}\to \gamma$. The analysis is based on the light-cone path integral approach to the induced radiation. Our results agree with that by Arnold, Moore and Yaffe obtained using the real-time thermal perturbation theory. It is demonstrated that the solution of the AMY integral equation is nothing but the time-integrated Green's function of the light-cone path integral approach written in the momentum representation.Comment: 12 pages, 2 figure

On consistency of hydrodynamic approximation for chiral media

We consider chiral liquids, that is liquids consisting of massless fermions and right-left asymmetric. In such media, one expects existence of electromagnetic current flowing along an external magnetic field, associated with the chiral anomaly. The current is predicted to be dissipation-free. We consider dynamics of chiral liquids, concentrating on the issues of possible instabilities and infrared sensitivity. Instabilities arise, generally speaking, already in the limit of vanishing electromagnetic constant, $\alpha_{el}\to 0$. In particular, liquids with non-vanishing chiral chemical potential might decay into right-left asymmetric states containing vortices.Comment: Published versio

Instability and Evolution of Nonlinearly Interacting Water Waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large amplitude freak waves in deep water.Comment: 4 pages, 4 figures, to appear in Physical Review Letter