@InProceedings{sen78a,
  author =       {Abhijit Sen and Charles F. F. Karney and Abraham Bers
                  and Nino R. Pereira},
  title =        {Complex Modified {K}orteweg--{D}e{V}ries Equation and
                  Nonlinear Propagation of Lower Hybrid Waves},
  preprint =     {M.I.T. Rept. \eref{PRR-78-6}{RLE PRR 78/6} (Feb. 1978)
                  4 pp.},
  booktitle =    {Proc. Third Topical Conf. on Radio Frequency Plasma
                  Heating},
  year =         1978,
  month =        jan,
  paper =        {G7},
  note =         {Meeting held at California Institute of Technology,
                  Pasadena, CA, Jan. 11--13},
  abstract =     {The nonlinear steady state propagation of lower hybrid
                  waves in a uniform plasma can be described by a
                  “Complex” Modified Korteweg-DeVries
                  equation, <i>v</i><sub>&tau;</sub> +
                  (|<i>v</i>|<sup>2</sup><i>v</i>)<sub>&xi;</sub> +
                  <i>v</i><sub>&xi;&xi;&xi;</sub> = 0, where <i>v</i>
                  the amplitude of the electric field is complex.  This
                  equation is not amenable to analytic solution by the
                  inverse Scattering Transform method and we solve it
                  numerically.  In the limit of a narrow spectrum
                  excitation at the boundary it approximately reduces to
                  the nonlinear Schr&ouml;dinger equation and we obtain
                  envelope soliton solutions.  For broader spectrums we
                  obtain &ldquo;MKDV type solitons&rdquo; with constant
                  phases.  We discuss these solutions in terms of
                  satisfying the radiation condition inside the plasma
                  and the limitations posed on the choice of
                  &ldquo;initial&rdquo; conditions by nonlinear
                  reflections.}
}