Nonlinear theory of non-axisymmetric resonant slow waves in straight magnetic flux tubes

Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weak ly dissipative isotropic plasmas for a cylindrical equilibrium model. The e quilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic ( SMA) waves are derived. Using the method of matched asymptotic expansions i nside and outside the narrow dissipative layer, we generalize the connectio n formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These nonlinear connection formulae in di ssipative cylindrical MHD are an important extention of the connection form ulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (19 91)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdelyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD deriv ed in slab geometry [Ruderman et, al., Phys. Plasmas 4, 75 (1997)]. These g eneralized connection formulae enable us to connect the solutions at both s ides of the dissipative layer without solving the MHD equations in the diss ipative layer. We also show that the nonlinear interaction of harmonies in the dissipative layer is responsible for generating a parallel mean flow ou tside the dissipative layer.