THEORY OF SOLITON TRANSITION FROM LOWER TO HIGHER DIMENSION

Recently Frycz and Infeld performed a numerical calculation that yielded a stage-by-stage picture of a spontaneous transition from flat to an array of cylindrical solitons [Phys. Rev. Lett. 63, 384 (1989)]. The model used was the Zakharov-Kuznetsov equation for solitons in plasmas permeated by very strong magnetic fields. Subsequently, similar calculations were performed for another equation, that of Hasegawa and Mima [Su, Horton, Morrison, and Pavlenko (unpublished)]. In this Brief Report we look at some calculations that endeavor to explain both the collapse of a flat soliton, leading to cylindrical entities, and also the collapse of cylindrical solitons when instabilities along the axes are allowed. Saturation is found in some cases but not in others.