An open problem on supernonlinear waves in a two-component Maxwellian plasma

Abstract

An unsolved problem in Maxwellian plasmas is delineated as, supernonlinear waves (SNWs) cannot exist in Maxwellian plasmas with less than three components. The criteria to generate SNWs in plasmas are the occurrence of at least two minima separated by at least one maxima in the curve of corresponding potential energy. This research is about the existence of SNWs in a two-component electron-ion plasma with Maxwell distributed electrons. The possible range of Mach number on the existence of SNWs is also reported. Analytical forms of all possible solitary, solitary-cusp and supernonlinear periodic wave solutions are derived. This research lights the existence of SNWs in a two-component Maxwellian plasma, which was unsolved till its inception from 2011.