Study of propagation of linear and non-linear Alfvén-gravity waves in rotating medium

Travelling waves in an incompressible, infinitely conducting, inviscid fluid of variable density are investigated under the influence of a horizontal magnetic field and Coriolis force. Periodic solutions are found in the limit of infinite vertical wave length. Phase diagrams are drawn to show the solution.

► Highly non-linear inhomogeneous partial differential equations can be analysed in phase plane via travelling wave solutions.
► Earth's rotation and magnetic field will not introduce any new singularities to the wave propagation in Earth's core.
► Waves are periodic when we consider no propagation in vertical direction.
► Non-linear equations can be linearised about the singular points and can also be analysed.
► This study can be used to predict periodic wave propagation in earthquakes.