Commuting Charges of the Quantum Korteweg-deVries and Boussinesq Theories from the Reduction of W(infinity) and W(1+infinity) Algebras

Integrability of the quantum Boussinesq equation for c=-2 is demonstrated by giving a recursive algorithm for generating explicit expressions for the infinite number of commuting charges based on a reduction of the W(infinity) algebra. These charges exist for all spins $s \geq 2$. Likewise, reductions of the W(infinity/2) and W((1+infinity)/2) algebras yield the commuting quantum charges for the quantum KdV equation at c=-2 and c=1/2, respectively.Comment: 11 pages, RevTe

The ultimate outcome of black hole - neutron star mergers

We present a simple, semi--analytical description for the final stages of mergers of black hole (BH) -- neutron star (NS) systems. Such systems are of much interest as gravitational wave sources and gamma--ray burst progenitors. Numerical studies show that in general the neutron star is not disrupted at the first phase of mass transfer. Instead, what remains of the neutron star is left on a wider, eccentric, orbit. We consider the evolution of such systems as they lose angular momentum via gravitational radiation and come into contact for further phases of mass transfer. During each mass transfer event the neutron star mass is reduced until a critical value where mass loss leads to a rapid increase in the stellar radius. At this point Roche lobe overflow shreds what remains of the neutron star, most of the mass forming a disc around the black hole. Such a disc may be massive enough to power a gamma--ray burst. The mass of the neutron star at the time of disruption (and therefore the disc mass) is largely independent of the initial masses of the black hole and neutron star, indicating that BH--NS star mergers may be standard candles.Comment: MNRAS, in pres