This test problem considers the propagation of a *Rossby soliton*
on an equatorial beta-plane, for which an
asymptotic solution exists to the inviscid, nonlinear shallow water
equations. In principle, the soliton should propagate westwards at
fixed phase speed, without change of shape. Since the uniform
propagation and shape preservation of the soliton are achieved through
a delicate balance between linear wave dynamics and nonlinearity, this
is a good context in which to look for erroneous wave dispersion
and/or numerical damping. A schematic diagram of the domain and
expected properties of the solution is shown in
Fig. 1.