Interaction and resonance of fast magnetoacoustic solitary waves in cylindrical geometry for dense astrophysical plasmas

Abstract

The cylindrical Kadomtsev-Petviashvili (CKP) equation, also known as Johnson's equation, is derived for dense electron ion plasmas in the small amplitude limit to study the interaction and resonance of two magnetoacoustic solitons in cylindrical geometry. The exact analytical solutions of the CKP equation are derived using Hirota's direct method and a novel gauge transformation. It is observed that cylindrical geometry transforms the line solitons to the horseshoe-like solitary structures. For multi-solitons, it is shown that the interaction parameter for the CKP solitary wave depends upon the plasma parameters of the system. For the present investigation, plasma parameters are chosen that are customarily found in the white dwarf stars. The interaction of magnetoacoustic solitons are shown to change their trajectory and introduce a phase shift. The resonance condition is developed for the CKP equation which shows that the amplitude of resultant solitons becomes four times the amplitude of initial solitons.