Weakly radiative spiral waves

The transition from the complex Ginzburg–Landau equation (CGLe) to the nonlinear Schrödinger equation (NLSe) in the analytically tractable weakly radiative limit is highly singular. This is strongly felt in the structure of spiral wave solutions of CGLe. The asymptotic wavenumber of the radiated wave is exponentially small in the effective “radiative” parameter q, but this value is attained only at exponentially large distances. This calls for great caution in application of perturbation schemes to detect various dynamic effects in weakly distorted spirals. The perturbation in q is expected to work well at moderately large, but not on exponentially large distances. After outlining the general perturbation scheme, we explore interactions of oppositely charged spirals and show that no bound pairs can be formed before interaction becomes exponentially weak.