We study the interaction of counter-propagating traveling waves in 2D nonequilibrium media described by the complex Swift-Hohenberg equation (CSHE). Direct numerical integration of CSHE reveal novel features of domain walls parallel to the wavevecors in 2D: wavevector selection and transverse instability. Analytical treatment is based on a study of coupled set of complex Ginzburg-Landau equations for counter-propagating waves. At the threshold we find the stationary (yet unstable) solution corresponding to the selected wavevectors of waves and solve linearized problem of its stability. 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. The results are in convincing agreement with 2D numerical simulations.
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