Charles Karney: Publication 10/85, Sen(1978a)

A. Sen, C. F. F. Karney, A. Bers, and N. R. Pereira.
Complex modified Korteweg-DeVries equation and nonlinear propagation of lower hybrid waves.
In Proc. Third Topical Conf. on Radio Frequency Plasma Heating, paper G7, January 1978.
M.I.T. Rept. RLE PRR 78/6 (Feb. 1978) 4 pp.
Meeting held at California Institute of Technology, Pasadena, CA, Jan. 11–13.
BibTeX Entry

The nonlinear steady state propagation of lower hybrid waves in a uniform plasma can be described by a “Complex” Modified Korteweg-DeVries equation, v_τ + (|v|²v)_ξ + v_ξξξ = 0, where v 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 Schrödinger equation and we obtain envelope soliton solutions. For broader spectrums we obtain “MKDV type solitons” 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 “initial” conditions by nonlinear reflections.