Research in physical applied mathematics, motivated by real world
problems is central to my investigations. My research is generally in
the field of nonlinear waves with a focus on two areas: 1) fluid
dynamics of dispersive media with accompanying wave excitations
including dispersive shock waves and solitary waves; 2) dynamics of
ferromagnetic media, spin torque, and localized excitations in
nanomagnetism. Methods employed include mathematical modeling,
analysis, asymptotics, Whitham modulation theory, and numerical
analysis. Whenever possible, comparisons with experiment are carried
Current research involves the construction and stability of dispersive
shock waves in single and multiple dimensions with applications to
boundary value problems in supersonic Bose-Einstein condensates,
nonlinear photonics, viscously deformable media (i.e. magma
migration), and shallow water waves.
This research is supported by the National
Science Foundation through an applied math individual investigator
grant DMS 1008973.
In the field of magnetodynamics, I am currently studying the
excitation of localized wave structures via the spin torque effect and
their coherent propagation. Numerical methods to compute
time-periodic, dynamic, localized structures are being pursued.
Seeking undergraduate and current/prospective
graduate students interested in studying nonlinear waves and
applications. Funding may be available.
Please contact me if you are
Manuscripts in Review
Shock waves in dispersive Eulerian fluids,
M. A. Hoefer.