Non-linear ring waves in a thin layer of magnetic fluid with variable thickness

A. N. Golubyatnikov

Lomonosov Moscow State University, Research Institute of Mechanics, 1 Michurinsky pr., 119192 Moscow, Russian Federation

Abstract
In the ``shallow water" approximation, the problem of propagation of non-linear ring waves with relatively small amplitudes in a thin layer of paramagnetic fluid with variable depth exposed to a non-uniform magnetic field is considered. The equations of motion that have a variational feature are derived. An exact method of solution for the problem with weak discontinuity has been developed. The problem with a weak shock wave is solved as an approximation to this solution. An example of wave propagation at the equilibrium initial state is considered. Figs 1, Refs 12.