  Symmetries of the one-dimensional shallow water magnetohydrodynamics
equations (SMHD) in Gilman's approximation are studied. The SMHD equations are
considered in case of a plane and uneven bottom topography in Lagrangian and
Eulerian coordinates. Symmetry classification separates out all bottom
topographies which yields substantially different admitted symmetries. The SMHD
equations in Lagrangian coordinates were reduced to a single second order PDE.
The Lagrangian formalism and Noether's theorem are used to construct
conservation laws of the SMHD equations. Some new conservation laws for various
bottom topographies are obtained. The results are also represented in Eulerian
coordinates. Invariant and partially invariant solutions are constructed.
