Nonlinear resonant slow magnetohydrodynamic (MHD) waves are
studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The
equilibrium 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 inside and outside
the narrow dissipative layer, we generalize the connection formulae for the Eulerian
perturbation of the total pressure and for the normal component of the velocity.
These nonlinear connection formulae in dissipative cylindrical MHD are an
important extention of the connection formulae obtained in linear ideal MHD [Sakurai
et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar
Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear
dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas 4, 75 (1997)].
These generalized connection formulae enable us to connect the solutions at both
sides of the dissipative layer without solving the MHD equations in the dissipative
layer. We also show that the nonlinear interaction of harmonics in the
dissipative layer is responsible for generating a parallel mean flow outside the dissipative