Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor

The integrability of an m-component system of hydrodynamic type, u_t=V(u)u_x, by the generalized hodograph method requires the diagonalizability of the mxm matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach to hydrodynamic chains -- infinite-component systems of hydrodynamic type for which the infinite matrix V(u) is `sufficiently sparse'. For such systems the Haantjes tensor is well-defined, and the calculation of its components involves finite summations only. We illustrate our approach by classifying broad classes of conservative and Hamiltonian hydrodynamic chains with the zero Haantjes tensor. We prove that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability.Comment: 36 pages, the classification results and proofs are refined. A section on generating functions is adde

Ordinary differential equations which linearize on differentiation

In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.Comment: 9 page

Classification of integrable hydrodynamic chains and generating functions of conservation laws

New approach to classification of integrable hydrodynamic chains is established. Generating functions of conservation laws are classified by the method of hydrodynamic reductions. N parametric family of explicit hydrodynamic reductions allows to reconstruct corresponding hydrodynamic chains. Plenty new hydrodynamic chains are found

The Upgraded D0 detector.

The DØ experiment enjoyed a very successful data-collection run at the Fermilab Tevatron collider between 1992 and 1996. Since then, the detector has been upgraded to take advantage of improvements to the Tevatron and to enhance its physics capabilities. We describe the new elements of the detector, including the silicon microstrip tracker, central fiber tracker, solenoidal magnet, preshower detectors, forward muon detector, and forward proton detector. The uranium/liquid-argon calorimeters and central muon detector, remaining from Run I, are discussed briefly. We also present the associated electronics, triggering, and data acquisition systems, along with the design and implementation of software specific to DØ