Excitation of dust-lower-hybrid wave and cusp solitons

A theoretical model is presented for the excitation of ultra-low frequency dust-lower hybrid mode (UDLH) by employing a relatively high frequency lower-hybrid wave as a pump and to examine its properties based on 3-wave resonant interaction. Modulational instability of the resulting UDLH wave is investigated and its growth rates are studied in two limiting cases. Additionally, one-dimensional nonlinear localized structures are obtained including bright and cusp solitons.