  In this thesis, we are concerned with the dynamics of spiral wave solutions
to Reaction-Diffsion systems of equations, and how they behave when subject to
symmetry breaking perturbations. We present an asymptotic theory of the study
of meandering (quasiperiodic spiral wave solutions) spiral waves which are
drifting due to symmetry breaking perturbations. This theory is based on
earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating
spirals, and the 1996 Biktashev et al theory of meander of spirals in
unperturbed systems. We combine the two theories by first rewriting the 1995
drift theory using the symmetry quotient system method of the 1996 meander
theory, and then go on to extend the approach to meandering spirals by
considering Floquet theory and using a singular perturbation method. We
demonstrate the work of the newly developed theory on simple examples. We also
develop a numerical implementation of the quotient system method, demonstrate
its numerical convergence and its use in calculations which would be difficult
to do by the standard methods, and also link this study to the problem of
calculation of response functions of spiral waves.
