Nonlinear lower-hybrid oscillations in a cold magnetized electron-positron-ion plasma

A new class of the exact nonlinear solutions for the lower-hybrid oscillations in a cold magnetized electron-positron-ion (e-p-i) plasma has been suggested by employing a method of Lagrange variables. It is found that the frequency of the lower-hybrid oscillations in an e-p-i plasma is approximately $sqrt{3}$ times the frequency of lower-hybrid oscillations in an electron-ion (e-i) plasma. The present work may have some relevance for laboratory/astrophysical e-p-i plasmas.