ONE-DIMENSIONAL, WEAKLY NONLINEAR ELECTROMAGNETIC SOLITARY WAVES IN APLASMA

The properties of one-dimensional, weakly nonlinear electromagnetic so litary waves in a plasma are investigated. The solution of the resulti ng eigenvalue problem shows that the solitary waves have amplitudes wh ich are allowed discrete values only and their vector and scalar poten tials are proportional to omega(p)/omega0 and (omega(p)/omega0)2, resp ectively, where omega(p), and omega0 are the plasma and electromagneti c wave frequencies, respectively. Their widths are comparable to the p lasma wavelength lambda(p) = 2pic/omega(p) where c is the velocity of light), except for the lowest-order solitary wave, whose width is larg e compared with lambda(p), which is a true wakeless solitary wave only in the limit of vanishing amplitude. Simple analytical solutions are derived for higher-order solitary waves, whose vector-potential envelo pe is highly oscillatory, and are shown to consist, in the group-veloc ity frame, of two trapped, oppositely traveling waves.