13 - Nonlinear Aspects

Summary

Nonlinear aspects of wave propagation are investigated. Special attention is given to magnetic slabs and tubes, deriving the Benjamin-Ono equation for the slow mode in a slab and the Leibovich-Roberts equation for the slow mode in a tube. Soliton solutions are obtained and illustrated under various solar conditions. The role of Whitham’s equation is explored. Dissipative effects are also added, and shown to lead to the Benjamin-Ono-Burgers equation. Approximate solutions are given and illustrated for solar conditions. The roles of viscous and thermal damping of weakly nonlinear slow waves (sound waves) are also explored, and the effect of gravity is examined. Both standing waves and propagating waves are looked at. Finally, the nonlinear kink mode is presented.