On the nature of radio filaments near the Galactic Center

We suggest that narrow, long radio filaments near the Galactic Center arise as kinetic jets - streams of high energy particles escaping from ram-pressure confined pulsar wind nebulae (PWNe). The reconnection between the PWN and interstellar magnetic field allows pulsar wind particles to escape, creating long narrow features. They are the low frequency analogs of kinetic jets seen around some fast-moving pulsars, such as The Guitar and The Lighthouse PWNe. The radio filaments trace a population of pulsars also responsible for the Fermi GeV excess produced by the Inverse Compton scattering by the pulsar wind particles. The magnetic flux tubes are stretched radially by the large scale Galactic winds. In addition to PWNe accelerated particles can be injected at supernovae remnants. The model predicts variations of the structure of the largest filaments on scales of $\sim$ dozens of years - smaller variations can occur on shorter time scales. We also encourage targeted observations of the brightest sections of the filaments and of the related unresolved point sources in search of the powering PWNe and pulsars.Comment: 5 pages, 2 figure

Integrable Dispersive Chains and Energy Dependent Schrodinger Operator

In this paper we consider integrable dispersive chains associated with the so called Energy Dependent Schrodinger operator. In a general case multi component reductions of these dispersive chains are new integrable systems, which are characterised by two arbitrary natural numbers. Also we show that integrable three dimensional linearly degenerate quasilinear equations of a second order possess infinitely many differential constraints. Corresponding dispersive reductions are integrable systems associated with the Energy Dependent Schrodinger operator

Transformations of integrable hydrodynamic chains and their hydrodynamic reductions

Hydrodynamic reductions of the hydrodynamic chain associated with dispersionless limit of 2+1 Harry Dym equation are found by the Miura type and reciprocal transformations applied to the Benney hydrodynamic chain

The Kupershmidt hydrodynamic chains and lattices

This paper is devoted to the very important class of hydrodynamic chains first derived by B. Kupershmidt and later re-discovered by M. Blaszak. An infinite set of local Hamiltonian structures, hydrodynamic reductions parameterized by the hypergeometric function and reciprocal transformations for the Kupershmidt hydrodynamic chains are described

Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains

Classification of the Egorov hydrodynamic chain and corresponding 2+1 quasilinear system is given in the previous paper. In this paper we present a general construction of explicit solutions for the WDVV equation associated with Hamiltonian hydrodynamic reductions of these Egorov hydrodynamic chain

The Hamiltonian approach in classification and integrability of hydrodynamic chains

New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is considered

Integrable hydrodynamic chains associated with Dorfman Poisson brackets

This paper is devoted to a description of integrable Hamiltonian hydrodynamic chains associated with Dorfman Poisson brackets. Three main classes of these hydrodynamic chains are selected. Generating functions of conservation laws and commuting flows are found. Hierarchies of these Hamiltonian hydrodynamic chains are extended on negative moments and negative time variables. Corresponding three dimensional quasilinear equations of the second order are presented

New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems

New Hamiltonian formalism based on the theory of conjugate curvilinear coordinate nets is established. All formulas are ``mirrored'' to corresponding formulas in the Hamiltonian formalism constructed by B.A. Dubrovin and S.P. Novikov (in a flat case) and E.V. Ferapontov (in a non-flat case). In the ``mirrored-flat'' case the Lagrangian formulation is found. Multi-Hamiltonian examples are presented. In particular Egorov's case, generalizations of local Nutku--Olver's Hamiltonian structure and corresponding Sheftel--Teshukov's recursion operator are presented. An number of Hamiltonian structures of all odd orders is found

Integrable hydrodynamic chains

A new approach for derivation of Benney-like momentum chains and integrable hydrodynamic type systems is presented. New integrable hydrodynamic chains are constructed, all their reductions are described and integrated. New (2+1) integrable hydrodynamic type systems are found.Comment: WARWICK CONFERENCE 2002 Geometry & Mechanics I

Modified dispersionless Veselov--Novikov equations and corresponding hydrodynamic chains

Various links connecting well-known hydrodynamic chains and corresponding 2+1 nonlinear equations are described