Abstract
This review is concerned with a recent development in the analytic theory of resonant Alfven waves in nonuniform magnetic flux tubes in the solar atmosphere. It discusses how an analytic study of simplified versions of the dissipative MHD equations for plasmas with high Reynolds numbers leads to the fundamental conservation law and simple analytic solutions for resonant Alfven waves. Asymptotic analysis of the analytic solutions gives jump conditions that connect the solutions across the dissipative layer. The analytic results enable us to understand the basic dynamics and energetics of resonant Alfven waves and help us with the interpretation of results of of numerical simulations in dissipative MHD. in addition, they make an accurate computation of resonant Alfven waves possible without having to solve numerically the dissipative MHD equations.
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