@Article{leclert79,
  author =       {Gerard P. Leclert and Charles F. F. Karney and
                  Abraham Bers and David J. Kaup},
  title =        {Two-Dimensional Self-modulation of Lower Hybrid Waves
                  in Inhomogeneous Plasmas},
  journal =      {Phys. Fluids},
  volume =       22,
  number =       8,
  pages =        {1545-1553},
  month =        aug,
  year =         1979,
  reprint =      {pf79b},
  preprint =     {M.I.T. Rept. \eref{PRR-77-25}{RLE PRR 77/25}
                  (Aug. 1977) 44 pp.},
  doi =          {10.1063/1.862774},
  abstract =     {For lower hybrid waves in an inhomogeneous plasma, the
                  two-dimensional self-modulation effects due to
                  ponderomotive force are studied under the assumption
                  that the field is electrostatic and has a narrow
                  <i>k</i> spectrum.  For a locally linear temperature
                  profile and a broad class of density profiles, exact
                  nonlinear solutions (solitons) are obtained by the
                  inverse scattering method.  The solitons decay and
                  spread as they propagate.  In addition to the usual
                  area condition on the potential &int; &phi;
                  <i>d</i>&xi; &ge; &pi;/2, inhomogeneity introduces a
                  second condition for solitons to occur.  It is shown
                  that this second condition is not satisfied in typical
                  tokamak plasmas, i.e., there is no soliton formation,
                  in contrast to the homogeneous case.  Furthermore, the
                  scaling of the threshold conditions with density and
                  temperature makes them more difficult to satisfy in
                  larger machines.}
}