Upper-hybrid solitons

Modulational instability and formation of envelope solitons of the upper-hybrid waves are considered. A more consistent calculation is given here which also includes the effect of ion inertia. A strong magnetic field can eliminate the existence of subsonic upper-hybrid solitons but can make possible the existence of supersonic upper-hybrid solitons. In order to describe the upper-hybrid solitons travelling at the speed of sound, the ion nonlinearity is included in the calculation with the assumption of charge neutrality in the low frequency plasma response. An exact soliton solution moving at the speed of sound is then exhibited. Finally, a fully nonlinear theory of the formation of envelope solitons of upper-hybrid waves is given. The assumption of charge neutrality in the low frequency plasma response is abandoned. The solution shows a smooth transition from a single-hump soliton as the Mach number increases to unity. Furthermore, the dip at the centre for the double-hump soliton is found to become smaller as the magnetic field becomes stronger.