Motion of spiral waves in the Complex Ginzburg-Landau equation

Details Motion of spiral waves in the Complex Ginzburg-Landau equation Motion of spiral waves in the Complex Ginzburg-Landau equation

2009-01-14

arxiv.org/abs/0901.1970v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres. In particular, the direction of the interaction changes from along the line of centres to perpendicular to the line of centres as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wavenumber and frequency are determined. These depend on the positions of the centres of the spirals, and so evolve slowly as the spirals move.

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