Non-linear waves in a thin layer of magnetic fluid

A. N. Golubiatnikov

Lomonosov Moscow State University, 1 Michurinsky pr., 119192 Moscow, Russia

Abstract
The problem of propagation of non-linear waves with a small amplitude in a thin layer of paramagnetic fluid with variable thickness in magnetic field is considered in shallow water theory. The equations of motion are derived and the method of solving the problem with weak discontinuity is developed. With the help of this method the problem with a weak shock wave is solved. An example of equilibrium initial state is considered.. Refs 7.