Boundary-value problem for the two-dimensional stationary heisenberg magnet with nontrivial background. II

The investigation of the boundary-value problem on a half-plane for the two-dimensional stationary Heisenberg magnet is continued. The asymptotic behavior of N-soliton solutions is discussed. The asymptotic contribution of the continuous spectrum is calculated. The gauge equivalence of the boundary-value problems for the models of a magnet and the elliptic equation represented by the sinh—Gordon equation is considered.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 513–529, September, 1995.     

The interaction force between rotating black holes at equilibrium

We study the previously constructed Riemann problem whose solutions correspond to equilibrium configurations of black holes. We evaluate the metric coefficients at the symmetry axis and the interaction force between the black holes. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 3, pp. 367–378, September, 1998.     

Equilibrium configuration of black holes and the inverse scattering method

The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizons must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 345–355, June, 1997.     

Quantum Integrable and Nonintegrable Nonlinear Schrödinger Models for Realizable Bose–Einstein Condensation in d+1 Dimensions (d = 1, 2, 3)

We evaluate finite-temperature equilibrium correlators for thermal time ordered Bose fields to good approximations by new methods of functional integration in d=1,2,3 dimensions and with the trap potentials V(r)0. As in the translationally invariant cases, asymptotic behaviors fall as to longer-range condensate values for and only for d=3 in agreement with experimental observations; but there are generally significant corrections also depending on due to the presence of the traps. For d=1, we regain the exact translationally invariant results as the trap frequencies 0. In analyzing the attractive cases, we investigate the time-dependent c-number Gross–Pitaevskii (GP) equation with the trap potential for a generalized nonlinearity –2c||²ⁿ and c<0. For n=1, the stationary form of the GP equation appears in the steepest-descent approximation of the functional integrals. We show that collapse in the sense of Zakharov can occur for c=0 and nd2 and a functional E _NLS[]0 even when V(r)0. The singularities typically arise as -functions centered on the trap origin r=0.