The Most Symmetric Drift Waves

Low frequency drift oscillations play an important role in the transport processes in magnetized plasmas, so they are intensely studied in recent decades [1]. The main problem in the drift waves investigations is the presence of nonlinear effects even at relatively small amplitudes. Nonlinear generation of the high space harmonics and their accumulation in the initial disturbance zone complicate numerical simulations of the drift waves evolution [2]. Thus some analytical approach based on symmetry analysis of the model is needed. In the present work, comparative symmetry analysis is carried out for Hasegava–Mima model for the drift waves in a plasma and for the well known Korteweg–de Vries (KdV) model. In the Section 2, symmetries and the most symmetric solutions of the KdV model are reviewed as an illustrative example. This model has sufficiently large symmetry for the existence of a family of the most symmetric stable solutions called solitons. In the Section 3, Hasegawa–Mima model symmetries and solutions are considered, both continuous and discrete symmetries are taken into account. General form of the most symmetrical solutions of the Hasegawa–Mima model is determined.