Domain Walls in Wave Patterns

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Abstract
We study the interaction of counterpropagating traveling waves in 2D nonequilibrium media described by the complex Swift-Hohenberg equation (CSHE). Direct numerical integration of CSHE reveals novel features of domain walls separating wave systems: wave-vector selection and transverse instability. Analytical treatment is based on a study of coupled complex Ginzburg-Landau equations for counterpropagating waves. At the threshold we find the stationary (yet unstable) solution corresponding to the selected waves. It is shown that sources of traveling waves exhibit long wavelength instability, whereas sinks remain stable. An analogy with the Kelvin-Helmholtz instability is established.