From nonassociativity to solutions of the KP hierarchy

A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A' a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200

Transverse momentum spectra of charged particles in proton-proton collisions at 1as=900 GeV with ALICE at the LHC

The inclusive charged particle transverse momentum distribution is measured in proton-proton collisions at s=900 GeV at the LHC using the ALICE detector. The measurement is performed in the central pseudorapidity region (|\u3b7|<0.8) over the transverse momentum range 0.15<10 GeV/c. The correlation between transverse momentum and particle multiplicity is also studied. Results are presented for inelastic (INEL) and non-single-diffractive (NSD) events. The average transverse momentum for |\u3b7|<0.8 is \u3008pT\u3009INEL=0.483\ub10.001 (stat.)\ub10.007 (syst.) GeV/c and \u3008pT\u3009NSD=0.489\ub10.001 (stat.)\ub10.007 (syst.) GeV/c, respectively. The data exhibit a slightly larger \u3008pT\u3009 than measurements in wider pseudorapidity intervals. The results are compared to simulations with the Monte Carlo event generators PYTHIA and PHOJET. \ua9 2010