Nonlinear theory of resonant slow MHD

Abstract. The nonlinear dynamics of resonant slow MHD waves in weakly dissi-pative plasmas is investigated in cylindrical geometry with a twisted equilibrium magnetic field. Linear theory has shown that the wave motion is governed by conser-vation laws and jump conditions across the resonant surface considered as a singu-larity – first derived in linear ideal MHD theory by Sakurai, Goossens and Hollweg [Solar Phys. 133, 227 (1991)]. By means of the simplified method of matched asymp-totic expansions, we obtain the generalized connection formulae for the variables across the dissipative layer, and we derive a non-homogeneous nonlinear partial differential equation for the wave dynamics in the dissipative layer. 1