Wigner Stability for the Uniaxial Incoherent Soliton in a Cold Plasma Under a Transverse Magnetic Field

Nonlinear equations governing the transmission of uniaxial waves in a cold plasma subjected to a transverse magnetic field is reduced to a nonlinear Schrödinger equation with the help of Krylov-Bogoliubov-Mitropolsky approach. The corresponding stability problem when the system is not fully coherent is analyzed with the help of Wigner transform. It is observed that the standard modulational stability is a special case of such analysis. The form of envelope soliton is obtained explicitly. The zones of stability are depicted explicitly as a function of plasma parameters. It is important to note that the nature of stability gets completely changed due to the presence of incoherence in the system. Finally, it may be mentioned that the frequency, growth rate, group velocity, and critical wavenumber show nontrivial dependence on the magnetic field.