Domain wall between traveling waves

A boundary (wall) separating two domains filled with traveling waves is considered within the framework of coupled Ginzburg-Landau (GL) equations with complex coefficients and group-velocity terms. The domain wall may be realized as a boundary produced in two dimensions by a collision of waves traveling in different directions, or as a sink or source of left- and right-traveling waves in one dimension. In the latter case the configuration is always symmetric, while in the former case it may be asymmetric. Under the assumption that the group velocities and imaginary parts of the coefficients in the GL equations are small, while the nonlinear coupling coefficient is close to 1, both symmetric and asymmetric solutions are obtained analytically. In particular, it is found that the sink must be broader than the source, which seems to agree with the recently reported experimental observations [P. Kolodner, Phys. Rev. A 46, 6431 (1992)] of the sinks and sources in traveling-wave convection, and that the wall uniquely selects the wave numbers of the colliding waves. In the asymmetric case, it is demonstrated that the boundary is moving at a certain velocity, which is also found.