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The oscillatory component of the transverse magnetoresistance of bismuth has been measured as a function of magnetic field orientation at liquid helium temperatures. A derivative technique was employed. In addition to sets of periods, observed in the de Haas-van Alphen effect by Shoenberg and by Brandt and attributed by them, respectively, to the electron and light-hole Fermi surfaces, we observe a new set of isotropic short periods, P = 0.72X10~5 G" 1 . The squares of the electron Fermi momenta w 0 /cn 2 , w 0 /c 2 2 2 , W0K33 2 , 7W0K23 2 are, respectively, 0.189, 45.4, 0.918, and -4.54 mo milli-electron volts (meV). For the light holes, moKu 2 and W0K33 2 are 1.51 and 21.0 Wo meV. For the new heavy carriers, w 0 «: 2 = 3.18 Wo meV. These data are fitted to two possible three-carrier models of the Fermi surface, and to a four-carrier model. Significant deviations of the oscillations from periodicity in H~l are observed for the electron part of the Fermi surface for certain magnetic field orientations.

We present what is to our knowledge the first general theory for describing interacting well-separated gray spatial solitons, propagating in an arbitrary self-defocusing nonlinearity. It reveals why two dark solitons will in general repel, becoming less dark as they propagate. The results are illustrated with analytic expressions for the Kerr and the saturating nonlinearities.