Soward is known for his work on
magnetohydrodynamics (MHD) and especially
dynamo theory, and also for his contributions to linear and nonlinear
stability theory. He used
asymptotic analysis to solve a number of outstanding problems in
applied mathematics. By a new pseudo-Lagrangian technique for studying lightly
damped fluid systems, he elucidated previously inexplicable features of Braginskii's geodynamo. Soward has provided explicit examples of steady
fast dynamo action, thus disproving a conjecture that such dynamos did not exist. He identified new rotating
modes of nonlinear
convection in rotating systems, and in collaboration with
Steven Childress, established an MHD dynamo model in a rapidly rotating
Bénard layer; he also gave the first demonstration that situations exist where oscillatory MHD dynamos generate
magnetic fields more readily than steady flows can. He collaborated with
Eric Priest to provide the first mathematically consistent account of the
Petschek mechanism of
magnetic field line reconnection. Soward also gave the first complete solution of the
Stefan (freezing) problem in cylindrical geometry; with C.A. Jones, he provided the first completely correct solution of the spherical
Taylor problem. == Awards and honours ==