Temporal evolution of nonlinear lower hybrid waves

The nonlinear evolution of a single lower hybrid waves in two dimensions and time is considered. If the potential is taken to have the form phi(x,z,t) exp(-iωt), the equation describing the fields is ivsub(tau) - ∫vsub(xi)dzeta + vsub(zeta zeta) + |v|2v = 0 where v is proportional to the electric field tau to time, and xi and zeta are distances along and across the lower hybrid ray. The properties of this equation are investigated numerically. When the amplitude of the injected lower hybrid waves is sufficiently large, the following phenomena are observed: the fields do not reach a steady state even though steady-state boundary conditions are imposed; the density modulations are sufficient to cause an appreciable fraction of the incident power to be reflected; the average wavenumber of the transmitted wave is larger than of the incident wave