Theory of interaction and bound states of spiral waves in oscillatory media

We present an alternative method for the calculation of the interaction between spirals in oscillatory media. This method is based on a rigorous evaluation of the perturbation of an isolated spiral resulting from neighboring spirals in a linear approximation. For the complex Ginzburg-Landau equation, the existence of bound states is identified with the parameter range where the perturbations behave in an oscillatory manner. The results for the equilibrium distance for two spirals in the bound state and also the dependence of the velocity of the spiral on the distance are in good agreement with numerical simulations. In the equally charged case, we find multiple bound states which may be interpreted as multiply armed spirals. Outside the oscillatory range, well-separated spirals appear to repel each other regardless of topological charge.