Analytical approach to the drift of the tips of spiral waves in the complex Ginzburg-Landau equation

In this paper, we investigate the motion of spiral waves in the complex Ginzburg-Landau equation (CGLE) analytically and numerically. We find that the tip of the spiral wave drifts primarily in the direction of the electric field and there is a smaller component of the drift that is perpendicular to the field when a uniform field is applied to the system. The velocity of the tip is uniform and its component along the electric field is equal to the strength of the field. When the CGLE system is driven by white noise, a diffusion law for the vortex core of the spiral wave is derived at long time explicitly. The diffusion constant is found to be [Formula presented] in which T is the noise strength and C is the core asymptotic factor of the spiral wave. When the external force is a simple oscillation we find that the tip of the spiral wave drifts if the frequency of the external force is the same as that of the system. Our analytical results are verified using numerical simulations.